$\left \{ {{x1+x2=-\frac{m-2}{2} } \atop {3x1=-\frac{m-2}{2}}} \right.$
<=>$\left \{ {{-\frac{m-2}{6}+x2=-\frac{m-2}{2} } \atop {x1=-\frac{m-2}{6}}} \right.$
<=>$\left \{ {{x2=-\frac{m-2}{2}+\frac{m-2}{6}=\frac{2-m}{3}} \atop {x1=-\frac{m-2}{6}}} \right.$
<=> x1.x2 = $\frac{(m-2)^2}{18}$=$\frac{-m}{2}$
<=> -9m=m^2-4m+4
<=> m^2+5m+4=0
<=> \(\left[ \begin{array}{l}m=-1\\m=-4\end{array} \right.\)