\(x\left(-4+3x+x^2\right)=0\)
\(\Leftrightarrow x\left(x^2+4x-x-4\right)=0\)
\(\Leftrightarrow x\left[x\left(x+4\right)-\left(x+4\right)\right]=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-4\end{matrix}\right.\)
