Can this matrix equation be solved?

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I have a matrix equation of the form

[Z][C][Z] - [Z][D] = [A][Z] - [B]

and I need to solve for [Z]. Is it possible? If so, what is the solution?

The matrices are all general, complex, with no specific known properties other than they are all square and of the same number of entries.

The form vaguely reminds me of an eigenvalue expression, but I don't see how that could help.