\(\left(2x^2-1\right)^2-2\left(2x^2-1\right)+1=0\Leftrightarrow\left(2x^2-1-1\right)^2=0\)\(\Leftrightarrow\left(2x^2-2\right)^2=0\)
\(\Rightarrow2\left(x^2-1\right)=0\)
\(\Rightarrow2\left(x+1\right)\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x+1=0\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)