\(\left(2x+1\right)^2-\left(x-2\right)^2=0\)
\(\left(2x+1-x+2\right)\left(2x+1+x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1-x+2=0\\2x+1+x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\3x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=\dfrac{1}{3}\end{matrix}\right.\)