solve

Etymology

From Middle English solven, from Latin solvō.

verb

1. To find an answer or solution to a problem or question; to work out.
   God shall solve the dark decrees of fate. 1649, Thomas Tickell, Thoughts occasioned by the sight of an original picture of King Charles I taken at the time of his trial
   A “moving platform” scheme[…]is more technologically ambitious than maglev trains even though it relies on conventional rails. Local trains would use side-by-side rails to roll alongside intercity trains and allow passengers to switch trains by stepping through docking bays. This set-up solves several problems […]. 2013-06-01, “Ideas coming down the track”, in The Economist, volume 407, number 8838, page 13 (Technology Quarterly)
2. to find out the perpetrator, the motive etc (of crime)
   to solve a murder   to solve a crime
3. (mathematics) To find the values of variables that satisfy a system of equations and/or inequalities.
4. (mathematics) To algebraically manipulate an equation or inequality into a form that isolates a chosen variable on one side, so that the other side consists of an expression that may be used to generate solutions.
5. (transitive) To loosen or separate the parts of.

noun

1. (now rare, chiefly law enforcement) A solution; an explanation.
   KEVIN: I decided a long time ago that just because I love Raymond, doesn't mean I have to love the people he works with. Good solve, Detective. 2014 February 4, The Party, Gil Ozeri and Gabe Liedman (writers), Michael Engler (director), Brooklyn Nine-Nine, season 1, episode 16
   “Hey, Mr. Quilt Bandit.” Ian smiled. “Nice solve, Nancy Drew.” 2017, Elodia Strain, The Dating Experiment