 This randomized phase III trial studies carboplatin, paclitaxel, and sorafenib tosylate to see how well they work compared to carboplatin and paclitaxel in treating patients with stage III or stage IV melanoma that cannot be removed by surgery. Drugs used in chemotherapy, such as carboplatin and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Sorafenib tosylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth and by blocking blood flow to the tumor. It is not yet known whether giving carboplatin and paclitaxel together with sorafenib tosylate is more effective than carboplatin and paclitaxel in treating melanoma. 