Whenever you have and equation in "x", you have an infinite number of equations!
While setting coeffients in is probablt simples, another way would be to subtract from both sides of the equation to get and use the fact that the only way a polynomial can be identically 0 (0 for all x) is if the coefficients are all 0, giving the same equations.
The most basic way, and the reason I said "an infnite number of equations", is to just put whatever values of x you want into the equation:
With if x= 0, you have , with x= 1, , and with x= -1, . That also gives you three equations to solve for A, B, and C.