a) \(x\left(x-2\right)+x-2=0\\ \Leftrightarrow\left(x-2\right)\left(x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
b) \(5x\left(x-3\right)-x+3=0\\ \Leftrightarrow5x\left(x-3\right)-\left(x-3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(5x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-3=0\\5x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{1}{5}\end{matrix}\right.\)
c)\(x\left(x-2\right)+5\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)
