Where in the Bible does it say that everything works out for good?

It doesn't say that. You are probably thinking of this verse:

"And we know that all things work together for good to them that love God, to them who are the called according to [his] purpose." (Romans 8:28)

There's a big qualifier there: it says this is true for people who love God and are called to serve his purpose--not just for anybody.

Quite a few Bible verses like this are often quoted without mentioning the conditions that are set on them. The meaning changes a lot when you see the rest of the statement, doesn't it?