Work out (some of its meanings)

1. PHRASAL VERB : have inflects

If you work out a solution to a problem or mystery, you manage to find the solution by thinking or talking about it.

• Negotiators are due to meet later today to work out a compromise.     
• It took me some time to work out what was causing this.   
• =  figure out   

2. PHRASAL VERB

If you work out the answer to a mathematical problem, you calculate it.

• It is proving hard to work out the value of bankrupt firms' assets.     
• When asked what a £40.35 meal for five people would cost each diner, they were unable to work it out.   
• =  calculate   

.... Cobuild

1.  Accomplish by work or effort: 

• I think we can work out a solution to this problem. [1500s] 
  

2.  Find a solution for, solve: 

• They hoped to work out their personal differences. 
• Can you help me work out this equation? [Mid-1800s] 
  

3.  Formulate or develop: 

• We were told to work out a new plan.
• He's very good at working out complicated plots. [Early 1800s] 
  

...Am-Heritage Idioms