Second-order matrix equations

Question

Let $A\in\mathbb{R}^{n\times n}$, $B\in\mathbb{R}^{n\times p}$, $C\in\mathbb{R}^{q\times n}$ and $D\in\mathbb{R}^{q\times p}$ be known matrices. Denote by $I_n$ the identity matrix of size $n\times n$ and $0_n$ the zero column vector of size $n$. My problem is to solve the second-order matrix equations $\left[\begin{array}{cc} zI_{n}-A & -B \\ C & D \\ \end{array} \right]v=0_{n+q}$ where $z\in\mathbb{C}$ and $v\in\mathbb{R}^{n+p}$ are unknowns. Is there any algorithm that can obtain the solution set of this second-order matrix equation problem?