You expand the left hand side and collect terms of like order in x, then

you equate coefficients of like powers of x on each side of the equation

to give a set of three simultaneous equations in A, B and C.

Doing this we have:

5x^2 + 5x + 5 = (A+B)x^2 + (2A+B)x + (2B+C)

so we have:

..A +. B ..... = 5

2A + .B ..... = 5

...... 2B + C = 5

Which you now solve.

RonL