To wit, how does 'loosen, release' semantically shift to mean 'able to pay all one owes'?
1650s, "able to pay all one owes," from French solvent,
from Latin solventem (nominative solvens), present participle of solvere "to loosen, release, accomplish, fulfill,"
from PIE *se-lu-, from reflexive pronoun *s(w)e- (see idiom) + root *leu- "to loosen, divide, cut apart."
I'm discombublated how "the process of taking a problem apart step by step" relates to financial solvency, if they relate at all? I read about liquid metaphors in the world of finance.