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