The matrix equation AXB+CYD=E

A necessary and sufficient condition for the matrix equation $\text{AXB}\text{+}\text{CYD}\text{=}\text{E}$ to be consistent is established, and if it is, a representation of the general solution is given, thus generalizing earlier results concerning the equation $\text{AX}\text{+}\text{YB}\text{=}\text{C}$.