This is written in the language of mathematics, which is why the other answerers found it strange. As with some of your other questions, these seem to be extracts from papers written by pseudoscientists purportedly trying to apply 'scientific' rigour to 'social sciences' in places where it does not belong. The author of this paper probably had as poor an understanding when writing as you do in reading it, so don't worry too much if it seems like nonsense, that is because it is, and nobody on Italki can fix that.

I personally find that a very strange sentence and wonder if it was written by a non-native English writer. I could throw out some guesses, but they would be only guesses.

This is not a typical use of the word, and certainly not a phrasal verb. If we accept it as proper English, then "solve for" roughly means "find an answer aimed towards..." or "find an answer with the goal of..."