The equation is $x^2-4x=y^2-4y$ in the case where $x\ne y$. The answer is $x+y=4$.
I can start from $x+y=4$ and create the equation very easily, and I can substitute $x+4=y$ into the equation and show both sides are equal easily. I just don't get how I would find the answer if I didn't know it before hand, and all I had was the equation? Any advice?