Determine the value of the parameter m, for which each solution of equation $$mx ^ 2 - (m ^ 2 - 3m + 2) x + 2m - 6 = 0$$ is less than $2$.
I case when $m=0$:
$m=0\\-2x-6=0\\x=-3$
II case when $m\in R-0$:
$\left\{\begin{array}{l}\triangle>0\\x_1<2\\x_2<2\end{array}\right.$
Why can not I properly solve this equation?
Correct anwswer is $ (-\infty, 0] ∪ (1,5)$
Where is my error ? Thanks