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