\(\left(2x+1\right)^1=2x+1\)
\(2x+1=\left(2x+1\right):\left(2x+1\right)\)
\(2x+1=1\)
\(2x=0\)
\(x=0\)
\(\Leftrightarrow\left(2x+1\right)^2-\left(2x+1\right)=0\Leftrightarrow\left(2x+1\right)\left(2x+1-1=0\right)\Leftrightarrow2x\left(2x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\frac{1}{2}\end{cases}}\)