\(x\left(x-2022\right)-3x+6066=0\)
\(\Leftrightarrow x\left(x-2022\right)-3\left(x-2022\right)=0\)
\(\Leftrightarrow\left(x-2022\right)\left(x-32022\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2022=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2022\\x=3\end{matrix}\right.\)