\(\left[{}\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
`x(x-2)+x-2=0`
`=>(x-2)(x+1)=0`
`=>`$\left[\begin{matrix} x-2=0\\ x+1=0\end{matrix}\right.$
`=>`$\left[\begin{matrix} x=2\\ x=-1\end{matrix}\right.$
\(x\left(x-2\right)+\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)