How to solve $c^2={b^2}{\sin(C)^2}+(b\cdot \cos(C) - a)^2$ for C?

Question

What is $c^2={b^2}{\sin(C)^2}+(b\cdot \cos(C) - a)^2$ when solving for C?

I am trying to figure out a formula for finding the length of the third side of a triangle with two sides and an angle given, but I'm stuck at the last step.

I tried isolating both $\sin(C)$ and $\cos(C)$ ( $\cos(C) = \frac{a}{b} - \sqrt{\frac{c^2}{b^2}-\sin(C)^2}$ and $\sin(C) = \sqrt{-(\cos(C) - \frac{a + c}{b})(\cos(C) - \frac{a - c}{b})}$ respectively), but I have no idea how to get C by itself. I have been trying for hours and I have no idea what to do.