How to solve congruence equations like this one? $$ 93^2-x^2 \equiv 0\bmod{12^2} $$
What properties can I use to solve it?
Maybe I have chosen a complicated equation, but, if you wish, you can choose another similar equation. The important thing, for me, is the method of resolution.
Using the Chinese remainder theorem,
$$x^2\equiv93^2\equiv3^2\bmod144\iff x^2\equiv0 \bmod 9\land x^2\equiv9\bmod16$$
$$\iff x\equiv0\bmod3\land x\equiv\pm3\bmod8\iff x\equiv\pm3\bmod24$$