How to solve the following linear matrix equation $A_1.X.A_2+B_1.X.B_2=C$?

64 Views Asked by At

How to solve $A_1 \cdot X \cdot A_2+B_1 \cdot X \cdot B_2=C$ for $X$?

I mean, is there a method to convert it into standard form $M \cdot X=N$?

Or other way said, is it possible to express $X$ in terms of $A_1$, $A_2$, $B_1$, $B_2$ and $C$?

I can solve the equation by converting it into system of ordinary linear equations, but want to find a more elegant method.