In the novel The Great Gatsby, there arose many problems. What exactly were the solutions to those problems, if any?

A vague question, but I'll try...

Fitzgerald's focus seems to be on the problem of America: Gatsby sees it as Dreamland--a place of promise, where a boy can go from rags to riches.  George Wilson sees it as a false promise: instead of owning a nice car, he must work on rich guys' cars in the Valley of Ashes.  So, the American dream is both an opportunity and a false promise.  Both of these men die, so Fitzgerald probably sides with the latter.

Fitzgerald also focuses on the problems of the master class: the rich elitists, the bourgeoisie, the East Eggers, the Buchanans.  Nick says Gatsby is better than the whole damn bunch of them put together.  He's not really.  Fitzgerald portrays all of the rich as careless people: they beat women, have affairs, are terrible parents, cheat on their spouses, hide behind their money, cheat at golf, drink too much, are terrible drivers, cause accidents.

Fitzgerald does not provide solutions; he is too smart for that.  And Fitzgerald was in no position to give any: he was as wild and reckless as any.  Gatsby is a great American novel written by someone who would live as an ex-patriot in Europe and die young, like Gatsby.  The novel provides an up-close look at an ugly America that most Americans don't want to see.