OK, I understand that part now, but I have another question:
Can somebody explain to me why equating coefficients work?
Example:
8x^3+13x = Ax^3 + 2Ax + Bx^2 + 2B + Cx + D
expanded into:
8x^3 + 13x = Ax^3 + Bx^2 + (2A+C)x + 2(B+D)
where A,B,C,D are constants.
Why does 8 = A; 0 = B; 13 = 2A...