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Applying multiple forces to one object and calculate net movement and rotation?

I'm working on a small game as a hobby project, and I've run into a problem that would seem simple, to me, but that I can't find any information on or solution to.

Multiple force on one object

How would one go about figuring out what happens to this object, in terms of movement and rotation?

I have a lot of (bad) ideas, but I think I'll hold them back and just leave it at that. This is my first post here, sorry if it's inappropriate etc. (Please let me know.)

(PS. Yes, it's a space game with small ships with many engines : )