\(x^2-3x+\left(x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow x\left(x-3\right)+\left(x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x+1=0\\x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=3\end{cases}}\)