"It is not going to work."
Translation:Det kommer inte att fungera.
I think they are sometimes used for expressing the same outcome but they are different.
Inte att fungera: Let's say a thought through solution (active choice) will not solve our problem or is not going to work. This is more a fact.
Inte att ordna sig: Is more like the coming events (passive choice) is not going to fix the problem by itself. I would say att "det ordnar sig" and "det löser sig" are more similar in this sense. This is more a feeling.
I hope this helps :)