This is a socalled "*nonsymmetric algebraic Ricatti equation*", which can be solved following the method explained in <A HREF="http://epubs.siam.org/doi/pdf/10.1137/S0895479800375680">Nonsymmetric algebraic Riccati equations and Wiener–Hopf factorization for M-matrices</A> (2001). See also Federico Poloni's general exposition in <A HREF="https://arxiv.org/abs/1004.1500">Quadratic vector equations</A> (2010).