Neutral subspaces of complex matrices

Consider the quadratic matrix equation $X^TDX+AX+X^TB+C=0$, where all the matrices are square and have the same order $n$. With this equation, we associate a block matrix $M$ of the double order $2n$. the solvability of the equation turns out to be related to the existence of neutral subspaces of dimension $n$ for this matrix. Reasonably general conditions ensuring the existence of such subspaces are presented.