This randomized phase III trial is studying chemoembolization and sorafenib tosylate to see how well they work compared with chemoembolization alone in treating patients with liver cancer that cannot be removed by surgery. Drugs used in chemotherapy, such as doxorubicin hydrochloride, mitomycin, and cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Chemoembolization kills tumor cells by carrying drugs directly into the tumor and blocking the blood flow to the tumor. Sorafenib tosylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether giving chemoembolization together with sorafenib tosylate is more effective than chemoembolization alone in treating patients with liver cancer