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