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It is proven that the solvability of these equations is equivalent to the solvability of some auxiliary standard Stein equations in the form of $W=\\mathcal{A}W\\mathcal{B}+\\mathcal{C}$ where the dimensions of the coefficient matrices $\\mathcal{A},\\mathcal{B}$ and $\\mathcal{C}$ are the same as those of the original equation. 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It is proven that the solvability of these equations is equivalent to the solvability of some auxiliary standard Stein equations in the form of $W=\\mathcal{A}W\\mathcal{B}+\\mathcal{C}$ where the dimensions of the coefficient matrices $\\mathcal{A},\\mathcal{B}$ and $\\mathcal{C}$ are the same as those of the original equation. 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