a) `(x+4)(3x-5)=0`
$⇔\left[ \begin{array}{l}x+4=0\\3x-5=0\end{array} \right.`⇔\left[ \begin{array}{l}x=-4\\3x=5\end{array} \right.`⇔\left[ \begin{array}{l}x=-4\\x=\dfrac53\end{array} \right.`$
b) `x^2 - 10x + 2x - 20 = 0`
`⇔ (x^2 - 10x )+ (2x - 20 )= 0`
`⇔x(x - 10 )+ 2(x - 10 )= 0`
`⇔(x - 10 )(x+2)= 0`
$\left[{}\begin{matrix}x-10=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.$
c) `2x^ 2-7x +3=0 `
`⇔2x^2-x-6x +3=0`
`⇔(2x^2-x)-(6x-3)=0`
`⇔x(2x-1)-3(2x-1)=0`
`⇔(x-3)(2x-1)=0`
$⇔\left[{}\begin{matrix}x-3=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\2x=1\end{matrix}\right.⇔\left[ \begin{array}{l}x=3\\x=\dfrac12\end{array} \right.$
