a) \(2x-1-3x\left(2x-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)-3x\left(2x-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(1-3x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\1-3x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
b) \(5\left(x-1\right)+x\left(1-x\right)=0\)
\(\Leftrightarrow5\left(x-1\right)-x\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(5-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\5-x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=5\end{matrix}\right.\)
c) \(2x^2+4x=0\)
\(\Leftrightarrow2x\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)