1,\(x\left(x-3\right)+x-3=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-3\right)=0\)

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

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

\(\Leftrightarrow5x\left(x-2\right)-\left(x-2\right)=0\)

\(\Leftrightarrow\left(5x-1\right)\left(x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}5x-1=0\\x-2=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=2\end{matrix}\right.\)

1,x(x − 3) + x − 3 = 0

=> (x - 3)(x + 1) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\)

​\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)