You know the mission were you kill kellog and you have the option to join the brotherhood? Well I did and it is pretty fun.... But when I discovered the institute HQ I Thought it was way cooler. (no offense) so I signed up! but now I come at a point were I want to be in the institute but not the brotherhood. I tried but I can't leave it. I don't want to erase my data back before I even joined the BOS because that would be 10 hours wasted! can someone help me?

Where can I find the institute?

If you didn't start the Mass Fusion quest you're fine.

I'm not sure. What's the mas fusion mission about? How can it be triggered so that I make sure I don't. I'm very curious about joining the institution

If you look in your quest log, it should be marked in the "completed" section if you did it. Whatever side you pick for the quest, you'll get a message saying the other faction will be permanently hostile. If you aren't there yet you're fine. I suggest saving at that point though so you can go back and complete the other ending.