$(x-1)(x-mx+2)=0$
⇔\(\left[ \begin{array}{l}x-1=0\\x-mx+2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=1\\x.(1-m)+2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=1\\x.(1-m)=-2\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=1\\x=\dfrac{-2}{1-m} (m\neq1)\end{array} \right.\)