$$ \begin{aligned} 0 &= m\cdot3-4m+m\cdot2-m+1&& \text{simplify right side} \\[1 em]0 &= -m+m+1&& \\[1 em]0 &= 1&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 1 } $ is FALSE, we conclude that the equation has no solution.
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