In this paper we deal with special sequence space equations (SSE) with operators, which are determined by an identity whose each term is a sum or a sum of products of sets of the form $\chi_a(T)$ and $\chi_{f(x)}(T)$ where $f$ map $U^+$ to itself and $\chi$ is any of the symbols $s$, $s^0$, or $s^{(c)}$. Among other things under some conditions we solve (SSE) with operators $\chi_a(C(\lambda)D_{\tau})+\chi_x(C(\mu)D_{\tau})=\chi_b$, and $\chi_a(C(\lambda)C(\mu))+\chi_x(C(\lambda\sigma)C(\mu))=\chi_b$ where $\chi\in\{s,s^0\}$, and $\chi_a(C(\lambda)D_{\tau})+s_x^0(C(\mu)D_{\tau}) =\chi_b$ where $\chi$ is either of the symbols $s$, or $s^{(c)}$ and $C(\nu)D_{\tau}$ is a factorable matrix.