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