a) $x^3-7x+6=0$

$\Rightarrow x^3-2x^2+2x^2-4x-3x+6=0$

$\Rightarrow x^2\left(x-2\right)+2x\left(x-2\right)-3\left(x-2\right)=0$

$\Rightarrow\left(x-2\right)\left(x^2+2x-3\right)=0$

$\Rightarrow\left(x-2\right)\left(x^2+3x-x-3\right)=0$

$\Rightarrow\left(x-2\right)\left[x\left(x+3\right)-\left(x+3\right)\right]=0$

$\Rightarrow\left(x-2\right)\left(x+3\right)\left(x-1\right)=0$

$\Rightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\\x-1=0\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\\x=1\end{matrix}\right.$

b) $2\left(x-3\right)-x^2+3x=0$

$\Rightarrow2\left(x-3\right)-x\left(x-3\right)=0$

$\Rightarrow\left(x-3\right)\left(2-x\right)=0$

$\Rightarrow\left[{}\begin{matrix}x-3=0\\2-x=0\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=3\\x=2\end{matrix}\right.$