\(\left(2x+1\right)^4=\left(2x+1\right)^6\\ \Rightarrow\left(2x+1\right)^6-\left(2x+1\right)^4=0\\ \Rightarrow\left(2x+1\right)^4\left[\left(2x+1\right)^2-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(2x+1\right)^4=0\\\left(2x+1\right)^2-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x+1=0\\\left(2x+1\right)^2=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\2x+1=1\\2x+1=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=0\\x=-1\end{matrix}\right.\)
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