I am having trouble with the following matrix equation:

$(K + MU)(K + MU) = U $

$K$, $M$, and $U$ are all square matrices, the values of $K$ and $M$ are known (but they don't have a particularly simple form, e.g. they are not diagonal). I would like to find a solution for $U$.

Does anyone know how this can be done? Thanks a lot!