Question

x(x-2)+x-2=0

Answer 1

x(x - 2) + x - 2 = 0

<=> x(x - 2) + (x - 2) = 0

<=> (x + 1)(x - 2) = 0

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

<=> \(\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)

Answer 2

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

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

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