If you broke it down correctly then you are left with :
(Then solve the system)
EDIT : how could I not think about system of equations ? I lack imagination so badly ...
Nice job factoring. I have no idea how you did that.
You aren't going to get a set (x, y) for these. From the first factor you get
(I'll let you take care of the cancellations.)
This linear relationship gives you a list of zeros of this equation. The other factor gives you a similar solution.
You may, of course, pick out a specific zero. For example, we can pick out x = 0 and we have the zero
-Dan
If you're looking at solving your linear Diophantine equations, here's a site that might help
LINEAR DIOPHANTINE EQUATIONS