This phase I trial studies the side effects and best dose of talazoparib when given together with carboplatin and paclitaxel in treating patients with solid tumors that have spread to other places in the body or cannot be removed by surgery. Talazoparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. 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, by stopping them from dividing, or by stopping them from spreading. Giving talazoparib with carboplatin and paclitaxel may kill more tumor cells.