I trying to solve for a function inside a finite summation and haven't been able to find many resources on the topic. Below is the general form of the equation and I'd like to rearrange it so solve for the function $f(n)$. It seems like there should be some theorem about this form but I can't seem to find anything. Thanks.
$$x=\sum_{n=1}^{N}g(n)f(n)$$