Solving for Christoffel Symbol

tmiddlet

I am attempting to solve for the Christoffel Symbol using the metric tensor.

I have gotten this far, but I don't know how to proceed with this equation. Any help would be appreciated!

[tex]-\frac{\partial g_{m'n'}}{\partial x^{p'}} = \Gamma^{mn}_{p'm'n'} g_{mn} + \Gamma^{nm}_{p'm'n'} g_{mn} [/tex]