This phase II trial studies the side effects and how well brentuximab vedotin and combination chemotherapy work in treating patients with CD30-positive peripheral T-cell lymphoma. Brentuximab vedotin is a monoclonal antibody, brentuximab, linked to a toxic agent called vedotin. Brentuximab attaches to CD30 positive cancer cells in a targeted way and delivers vedotin to kill them. Drugs used in chemotherapy, such as cyclophosphamide, doxorubicin, etoposide, and prednisone work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving brentuximab vedotin and combination chemotherapy may work better in treating patients with CD30-positive peripheral T-cell lymphoma.