\(\left(x-1\right)^{43}=\left(x-1\right)^{2021}\)
\(\Rightarrow\left(x-1\right)^{43}\left[\left(x-1\right)^{1978}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^{1978}=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\\x=0\end{matrix}\right.\)