\(\left(x^2+4x-1\right)^2=\left(x^2-4x+1\right)^2\)
\(\Leftrightarrow\left(x^2+4x-1\right)^2-\left(x^2-4x+1\right)^2=0\)
\(\Leftrightarrow\left(x^2+4x-1-x^2+4x-1\right)\left(x^2+4x-1+x^2-4x+1\right)=0\)
\(\Leftrightarrow\left(8x-2\right)2x^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=0\end{matrix}\right.\)