The verb solve has 3 senses (first 2 from tagged texts)
1. (31) solve, work out, figure out, puzzle out, lick, work -- (find the solution to (a problem or question) or understand the meaning of; "did you solve the problem?"; "Work out your problems with the boss"; "this unpleasant situation isn't going to work itself out"; "did you get it?"; "Did you get my meaning?"; "He could not work the math problem")
2. (5) resolve, solve -- (find the solution; "solve an equation"; "solve for x")
3. clear, solve -- (settle, as of a debt; "clear a debt"; "solve an old debt")