0 to do a calculation to get an answer to a mathematical question: --
1 to understand something or to find the answer to something by thinking about it: --
[ + that ] Investigators needed several months to work out that a fraud had been committed.
[ + question word ] There will be a full investigation to work out what caused the accident.
2 If a problem or difficult situation works out, it gradually becomes better or satisfactory, and if you work it out, you make it better or satisfactory: --