Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed AML, other than acute
             promyelocytic leukemia, as defined by the 2008 World Health Organization (WHO)
             criteria that have relapsed or refractory to standard chemotherapy; unsuitable for
             standard chemotherapy or unwilling to undergo standard chemotherapy; subjects >= 60
             years of age with newly diagnosed AML who are not candidates for or have refused
             standard chemotherapy are eligible

          -  Patients with prior autologous and allogeneic hematopoietic stem cell transplantation
             are eligible if patients are off immunosuppression for > 1 month and have no evidence
             of active graft versus host disease (GVHD) except grade 1 skin GVHD

          -  Positive for RAS mutation (neuroblastoma RAS viral [v-ras] oncogene homolog [NRAS]
             codon 12, 13, 61 mutation or Kirsten rat sarcoma viral oncogene homolog [KRAS] codon
             12, 13, 61 mutation) at a Clinical Laboratory Improvement Amendments (CLIA)-certified
             laboratory prior to study entry; mutational testing will be performed on bone marrow
             sample and/or peripheral blood; patients with previously known RAS mutations prior to
             study entry may be considered positive for RAS mutation for eligibility prior to a
             CLIA-certified laboratory confirmation of such a mutation at the discretion of the
             investigator; (appropriate blood and/or bone marrow samples must be taken for RAS
             determination and submitted to a CLIA-certified laboratory prior to study entry);
             however, if such a mutation is not confirmed by the M D Anderson Cancer Center
             (MDACC)/other center's CLIA-certified laboratory, the patient may be permitted to stay
             on the study if they wish and consent to do so but such patients' data will be
             analyzed separately

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  Life expectancy of greater than 4 weeks

          -  Able to swallow and retain orally-administered medication and does not have any
             clinically significant gastrointestinal abnormalities that may alter absorption such
             as malabsorption syndrome or major resection of the stomach or bowels

          -  All prior treatment-related toxicities must be Common Terminology Criteria for Adverse
             Events (CTCAE) version (v)4 grade =< 1 (except alopecia) prior to the first dose of
             the study drug

          -  Serum total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (isolated
             total bilirubin > 1.5 institutional ULN is acceptable if bilirubin is fractionated and
             direct bilirubin is < 35%)

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x
             institutional ULN

          -  Serum creatinine =< 1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault
             formula) >= 60 mL/min

          -  Fasting serum glucose =< 150 mg/dl (fasting is defined as at least 8 hours without
             oral intake)

          -  Left ventricular ejection fraction (LVEF) >= institutional lower limit of normal (LLN)
             AND at least 50%; LVEF can be assessed by either echocardiogram (ECHO) or multi gated
             acquisition scan (MUGA)

          -  Women of child-bearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control; abstinence) prior to study entry, during
             the study participation, and for four months after the last dose of drug; women of
             child-bearing potential must have a negative serum pregnancy test within 14 days prior
             to randomization and agree to use effective contraception throughout the treatment
             period and for 4 months after the last dose of study treatment; should a woman become
             pregnant or suspect she is pregnant while she or her partner is participating in this
             study, she should inform her treating physician immediately

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  History of another malignancy; exception: patients who have been disease-free for 3
             years, or patients with a history of completely resected non-melanoma skin cancer
             and/or patients with indolent secondary malignancies, are eligible; consult the Cancer
             Therapy Evaluation Program (CTEP) Medical Monitor if unsure whether second
             malignancies meet the requirements specified above

          -  History of interstitial lung disease or pneumonitis

          -  Any major surgery, extensive radiotherapy, chemotherapy with delayed toxicity,
             biologic therapy, or immunotherapy within 21 days prior to randomization; daily or
             weekly chemotherapy (with the exception of hydroxyurea) without the potential for
             delayed toxicity within 14 days prior to randomization unless there is evidence of
             rapidly progressive disease

          -  Use of other investigational drugs within 28 days (or five half-lives, whichever is
             shorter; with a minimum of 14 days from the last dose) preceding the first dose of
             trametinib/GSK2141795 and during the study

          -  Symptomatic or untreated leptomeningeal disease or brain metastases or spinal cord
             compression

          -  Patients with abnormal fasting glucose values (> 150 mg/dl) at screening will be
             excluded; in addition, patients with type 1 diabetes will also be excluded; however,
             patients with type 2 diabetes will be allowed if diagnosed >= 6 months prior to
             enrollment, and if presenting with regular hemoglobin A1C (HbA1C) =< 8% at screening

          -  Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs
             chemically related to trametinib or excipients or to dimethyl sulfoxide (DMSO) or
             GSK2141795

          -  Current use of a prohibited medication; the following medications or non-drug
             therapies are prohibited:

               -  Other anti-cancer therapy while on study treatment; (Note: megestrol [Megace] if
                  used as an appetite stimulant is allowed)

               -  Concurrent treatment with bisphosphonates is permitted; however, treatment must
                  be initiated prior to the first dose of study therapy; prophylactic use of
                  bisphosphonates in patients without bone disease is not permitted, except for the
                  treatment of osteoporosis

               -  The concurrent use of all herbal supplements is prohibited during the study
                  (including, but not limited to, St. John's wort, kava, ephedra [ma huang], gingko
                  biloba, dehydroepiandrosterone [DHEA], yohimbe, saw palmetto, or ginseng)

                    -  Note: for proliferative disease, hydroxyurea will be allowed during weeks 1
                       and 2 of cycle 1 of study; hydroxyurea may be started or the dose changed
                       during that 2-week period if it is clinically indicated; if a subject not
                       previously on a stable dose of hydroxyurea needs to begin hydroxyurea or a
                       subject on a stable dose needs to have their dose increased during the first
                       2 weeks, the investigator will notify the clinical team that this has been
                       initiated

          -  Drugs that potently inhibit cytochrome P450 family 3, subfamily A, polypeptide 4
             (CYP3A4) should either be prohibited or used with caution; drugs which are strong
             inducers of cytochrome P450 family 3, subfamily A (CYP3A) should also be prohibited;
             drugs that are substrates of CYP3A4 or cytochrome P450 family 2, subfamily C,
             polypeptide 8 (CYP2C8) with a narrow therapeutic index may be prohibited; drugs that
             are sensitive substrates of CYP3A4 or CYP2C8 should be used with caution; it is
             important to regularly consult a frequently-updated list; medical reference texts such
             as the Physicians' Desk Reference may also provide this information; as part of the
             enrollment/informed consent procedures, the patient will be counseled on the risk of
             interactions with other agents, and what to do if new medications need to be
             prescribed or if the patient is considering a new over-the-counter medicine or herbal
             product

          -  History or current evidence/risk of retinal vein occlusion (RVO)

          -  History or evidence of cardiovascular risk including any of the following:

               -  LVEF < institutional LLN or < 50%

               -  A QT interval corrected for heart rate using the Bazett's formula QTcB >= 480
                  msec

               -  History or evidence of current clinically significant uncontrolled arrhythmias
                  (exception: patients with controlled atrial fibrillation for > 30 days prior to
                  randomization are eligible)

               -  History or evidence of current clinically significant uncontrolled arrhythmias
                  (exception: patients with controlled atrial fibrillation for > 30 days prior to
                  study dose are eligible)

               -  Patient with symptomatic bradycardia, or a history of clinically significant
                  bradyarrhythmias such as sick sinus syndrome, second (2nd) degree
                  atrioventricular (AV) block (Mobitz type 2)

               -  History of acute coronary syndromes (including myocardial infarction and unstable
                  angina), coronary angioplasty, or stenting within 6 months prior to study dose

               -  History or evidence of current >= class II congestive heart failure as defined by
                  the New York Heart Association (NYHA) functional classification system

               -  Treatment-refractory hypertension defined as a blood pressure of systolic > 140
                  mmHg and/or diastolic > 90 mmHg which cannot be controlled by anti-hypertensive
                  therapy

               -  Patients with intra-cardiac defibrillators

               -  Known cardiac metastases

          -  Known active hepatitis B virus (HBV), or hepatitis C virus (HCV) infection (patients
             with chronic or cleared HBV and HCV infection, are eligible); patients with human
             immunodeficiency virus (HIV) are not eligible if on anti-retroviral medications

          -  Any serious/and or unstable pre-existing medical disorder (aside from malignancy
             exception above), psychiatric disorder, or other conditions that could interfere with
             subject's safety, obtaining informed consent or compliance to the study procedures

          -  The study drug must not be administered to pregnant women or nursing mothers; women of
             childbearing potential should be advised to avoid pregnancy and use effective methods
             of contraception; men with a female partner of childbearing potential must have either
             had a prior vasectomy or agree to use effective contraception; if a female patient or
             a female partner of a patient becomes pregnant while the patient receives
             trametinib/GSK2141795, the potential hazard to the fetus should be explained to the
             patient and partner (as applicable)

          -  HIV-positive patients on combination antiretroviral therapy are ineligible

          -  Hypoxia (oxygen saturation < 90% on room air) or in the opinion of the investigator
             any pulmonary compromise leading to hypoxia, at the time of study entry