Any reference on how to solve the problem $Ax + c = \lambda Bx$ , where $A$, $B$ are full rank matrices, $c$ and $x$ are vectors and $\lambda$ is an unknown constant. I want to solve for both $x$ and $\lambda$. Without the vector c, this is a Generalized Eigen problem and is easy to solve.

I actually don't need the value of $\lambda$ I care only about $x$. I just need a citation and I can follow it up.