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