\(\left(x+1\right)=\left(x+1\right)^2\)

\(\Rightarrow\left(x+1\right)-\left(x+1\right)^2=0\)

\(\Rightarrow\left(x+1\right)\left[1-\left(x+1\right)\right]=0\)

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