E.g. He sits down and figure out how many guests will attend the party.
"find out":to get information after trying to discover it or by chance.
E.g. Can anybody find out how much the car is going to cost?
IMO, "Study" emphasises the long tough process and efforts in pursuing knowledge of a particular subject or in a particular professional field. For example,
I am studying for a Ph. D. degree in literature in the UK.
I am studying regional variation in pine seed yields.
"Learn" focuses on gaining knowledge of a subject or skill by studying it, or by being taught and without going through a long hard process or efforts like "study". For example,
What did you learn in school this week?
The teacher told the pupils to learn the poem by heart.
(Not a teacher)
Student or Learner