Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 transitive v. To find a solution to.
 transitive v. To work out a correct solution to (a problem).
 intransitive v. To solve an equation: Insert the values of the constants and solve for x.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 v. To find an answer or solution to a problem or question; to work out.
 v. To find the values of variables that satisfy a system of equations and/or inequalities.
 v. 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.
 n. A solution; an explanation.
from the GNU version of the Collaborative International Dictionary of English
 n. A solution; an explanation.
 transitive v. To explain; to resolve; to unfold; to clear up (what is obscure or difficult to be understood); to work out to a result or conclusion.
from The Century Dictionary and Cyclopedia
 To loosen; disentangle; unravel; hence, to explain or clear up the difficulties in; resolve; explain; make clear; remove perplexity from: as, to solve a difficulty, a puzzle, or a problem.
 To determine; put an end to; settle.
 To determine or work out by rule; operate on by calculation or mathematical processes, so as to bring out the required result: as, to solve a problem in mathematics.
 To dissolve; melt.
 n. Solution.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 v. find the solution
 v. settle, as of a debt
 v. find the solution to (a problem or question) or understand the meaning of
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

Too often the result of such instruction is students who can add when told to add, or solve quadratic equations when told to �solve the following quadratic equations,� but cannot decide when to use these techniques in solving problems.

I want to travel, see the sites, maybe solve some  "She almost said _solve some murders_, but finished lamely,"  solve some problems in magnesium technology. "

Always, the main problem to solve is to help the user to find "the needle in the haystack".

A brilliant puzzle that no one can solve is called a “failure.”

Israel's foreign minister has suggested that France and Spain solve Europe's problems before lecturing his country on how to deal with the IsraeliArab conflict.

Levy also says that along with scheduling, figuring out the mystery that the grown up Hardy boys need to solve is also a key element to figure out before moving forward.

You won't, in short, solve anything by draconian bans, by wiping whole nations from the cricketing map.

The ultimate issue to solve is communities not functioning, it is the decline of communities and community integration that is also causing the decline of the pubs that rely on those communities.

But if the problem you are trying to solve is CO2 emissions then the only viable alternative is nuclear power.
Global Warming and the Minefield of Unintended Consequences  Freakonomics Blog  NYTimes.com

If the problem that you are trying to solve is dependence of foreign energy sources then cornethanol may be a viable solution.
Global Warming and the Minefield of Unintended Consequences  Freakonomics Blog  NYTimes.com
gangerh commented on the word solve
One of the simplest copy writing formulas is to state the customer's problem, tell them you can solve it and then tell them precisely how you're going to solve it.
'15 words that will make you money'
July 24, 2009
bilby commented on the word solve
What language is this?
April 19, 2009
yarb commented on the word solve
In North American sports reporting, to score against for the first time in a game:
"Taylor Pyatt finally solved Detroit netminder Chris Osgood at 2:27 of the second, pouncing on a loose puck after he and Kyle Wellwood forced little Wing Jiri Hudler into a turnover in his own slot area."
 Canucks ride high after fourth straight win, Vancouver Sun, 112508.
Taylor Pyatt, a great hockey name.
November 26, 2008