Do \(x^2-2x+3=\left(x-1\right)^2+2>0\) \(\forall x\) nên BPT tương đương:
\(-2\left(x^2-2x+3\right)< x^2-4x+m< 3\left(x^2-2x+3\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x^2-8x+m+6>0\\2x^2-2x+9-m>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\Delta'=16-3\left(m+6\right)< 0\\\Delta'=1-2\left(9-m\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-3m-2< 0\\2m-17< 0\end{matrix}\right.\) \(\Rightarrow\frac{-3}{2}< m< \frac{17}{2}\)