This is a socalled "nonsymmetric algebraic Ricatti equation", which can be solved following the method explained in Nonsymmetric algebraic Riccati equations and Wiener–Hopf factorization for M-matrices (2001). See also Federico Poloni's general exposition in Quadratic vector equations (2010).

This belongs to the class of "nonsymmetric algebraic Ricatti equations", which can be solved following the method explained in Nonsymmetric algebraic Riccati equations and Wiener–Hopf factorization for M-matrices (2001) and in Federico Poloni's paper on Quadratic vector equations (2010).