Irreducible Quadratic Factors (Partial Fractions)

Hello, I've been reading the examples in my text over and over and I'm having trouble solving problems with irreducible quadratic factors.

The problem: Find the constants in the partial fraction decomposition

(2x-3)/(x-2)((x^2)+4) = A/(x-2) + (Bx+C)/((x^2)+4)

I solved for A

2x+4 = A((x^2)+4) + (Bx+C)(x-2)

Setting x=2, 8 = 8A + 0

A=1

Then, like in the example in my text, I distributed the equation and grouped by x's

2x + 4 = (x^2) + 4 + B(x^2) - 2B + Cx - 2C

0 = (x^2)(1+B) + x(C-2) - 2(B-C)

This is where I am lost. I do not know how to solve for B or C.

Thanks!