problem-solve
/ˈprɒbləmˌsɒlv/verb
[no object] To find a solution to a difficult or complex question or situation; to engage in the actions or thoughts necessary to discover solutions to problems. Also with object: to think out, grapple with, or solve (a problem).
Origin
1950s; earliest use found in The New York Times. From problem + solve, after problem-solving adjective, problem-solver.