General:
* Resolve
* Unravel
* Decipher
* Answer
* Figure out
* Work out
* Crack (informal)
For problems:
* Address
* Tackle
* Deal with
* Overcome
* Fix
* Remedy
For puzzles:
* Solve
* Crack
* Decipher
* Unravel
* Deduce
For equations:
* Calculate
* Compute
* Determine
* Evaluate
For mysteries:
* Uncover
* Investigate
* Expose
* Reveal
Remember to choose the word that best fits the specific situation and meaning you want to convey.