\(\left(2x+1\right)\left|x-3\right|=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x+1=0\\\left|x-3\right|=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=3\end{cases}}\)
\(\left(x-\frac{1}{2}\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{2}=0\\2x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{3}{2}\end{cases}}\)