Accomplish by work or effort, as in I think we can work out a solution to this problem. [1500s] For work out all right, see turn out all right.
Find a solution for, solve, as in They hoped to work out their personal differences, or Can you help me work out this equation? [Mid-1800s]
Formulate or develop, as in We were told to work out a new plan, or He's very good at working out complicated plots. [Early 1800s]
Discharge a debt by working instead of paying money, as in She promised she'd work out the rest of the rent by baby-sitting for them. [Second half of 1600s]
Prove effective or successful, as in I wonder if their marriage will work out.
Have a specific result, add up, as in It worked out that she was able to go to the party after all, or The total works out to more than a million. [Late 1800s]
Engage in strenuous exercise for physical conditioning, as in He works out with weights every other day. [1920s]
Exhaust a resource, such as a mine, as in This mine has been completely worked out. [Mid-1500s]