\(\sqrt{\left(x+1\right)^2}=\sqrt{4.\left(x^2-2x+1\right)^2}^{ }\)
\(\Rightarrow x+1=2.\left(x^2-2x+1\right)^{ }\)
\(\Leftrightarrow\)x+1-2x^2 +2x -1=0
\(\Leftrightarrow\)-2x^2 +3x =0
\(\Leftrightarrow\)x.(-2x+3)=0\(\Leftrightarrow\)\(\orbr{\begin{cases}x=0\\x=\frac{3}{2}\end{cases}}\)