\(a,x^2-3x=0\)

\(x.\left(x-3\right)=0\)

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

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)

\(b,3x+2\left(5-x\right)=0\)

\(3x+10-2x=0\)

\(x+10=0\)

\(x=0-10\)

\(x=-10\)

\(c,2x^3-2x=0\)

\(2x\left(x^2-1\right)=0\)

\(2x.\left(x-1\right).\left(x+1\right)=0\)

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

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)

\(d,x^2-6x+5=0\)

\(x^2+x+5x+5=0\)

\(x.\left(x+1\right)+5.\left(x+1\right)=0\)

\(\left(x+1\right).\left(x+5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=-5\end{matrix}\right.\)

\(e,3x.\left(x-5\right)+2x-10=0\)

\(3x.\left(x-5\right)+2.\left(x-5\right)=0\)

\(\left(x-5\right).\left(3x+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=5\\3x=-2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=5\\x=-\dfrac{2}{3}\end{matrix}\right.\)

\(f,3x.\left(x-2022\right)-x+2022=0\)

\(3x.\left(x-2022\right)-\left(x-2022\right)=0\)

\(\left(x-2022\right).\left(3x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=2022\\3x=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2022\\x=\dfrac{1}{3}\end{matrix}\right.\)

\(a,6xy+12x-4y-8=\left(6xy+12x\right)-\left(4y+8\right)=6x\left(y+2\right)-4\left(y+2\right)=\left(y+2\right).\left(6x-4\right)=\left(y+2\right).2.\left(3x-2\right)\)

\(b,x^3+2x^2-x-2=\left(x^3+2x^2\right)-\left(x+2\right)=x^2.\left(x+2\right)-\left(x-2\right)=\left(x-2\right).\left(x^2-1\right)=\left(x-2\right).\left(x-1\right).\left(x+1\right)\)