$n$-dimensional quadratic equation $(Ax)x + Bx + c = 0$

Question

Given an $n\times n$ matrix $A$ and a vector $b$ of length $n$, many things are known about the solution of $Ax=b$. I'm now dealing with an $n$-dimensional equivalent of the quadratric equation, $$ (\mathbf{A}x)x + Bx + c = 0 $$ where $\mathbf{A}$ is an $n\times n \times n$ tensor, $B$ an $n \times n$ matrix and $c$ is a vector of length $n$. What's known about the solution(s) of the above equation? Is there perhaps a representation of solutions in terms of vector operations and square roots?