a)\(5x\left(x-1\right)-\left(1-x\right)=0\)
\(\Leftrightarrow5x\left(x-1\right)+\left(x-1\right)=0\)
\(\Leftrightarrow\left(5x+1\right)\left(x-1\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}5x+1=0\\x-1=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{5}\\x=1\end{matrix}\right.\)
b) \(\left(x-3\right)^2-\left(2x+3\right)^2=0\)
\(\Leftrightarrow\left(x-3+2x+3\right)\left(x-3-2x-3\right)=0\)
\(\Leftrightarrow3x\left(-x-6\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}3x=0\\-x-6=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x=-6\end{matrix}\right.\)
c)\(2x\left(x^2-4\right)=0\)
\(\Leftrightarrow2x\left(x+2\right)\left(x-2\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}2x=0\\x+2=0\\x-2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x=-2\\x=2\end{matrix}\right.\)
d)\(\left(x-2\right)^2-\left(x-2\right)\left(x+3\right)=6\)
\(\Leftrightarrow x^2-4x+4-x^2-3x+2x+6-6=0\)
\(\Leftrightarrow-5x+4=0\)
\(\Leftrightarrow x=\dfrac{4}{5}\)
e)\(x^2+6x-7=0\)
\(\Leftrightarrow x^2-x+7x-7=0\)
\(\Leftrightarrow x\left(x-1\right)+7\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+7\right)\left(x-1\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x+7=0\\x-1=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-7\\x=1\end{matrix}\right.\)