front brake / rear brakes

so, through carelessness and stupidity, i bought the wrong thing. So i believe the only difference between a front brake and a rear brake is the length of the bolt that runs through the brake mount, whether it be in the rear triangle or the fork.

If so, is there a way to change the bolt and make it longer, so i can run my stupid purchase of the rear brake to become a front brake?

You can pick up longer recessed nuts (painful) that will reach the shorter bolt.