Question

5x² - 3x - 8\(=0\)

Answer 1

\(5x^2-3x-8=0\\ =5x^2+5x-8x-8\\ =5x\left(x+1\right)-8\left(x-1\right)\\ =\left(5x-8\right)\left(x+1\right)\)

Answer 2

\(\Leftrightarrow5x^2+5x-8x-8=0\)

\(\Leftrightarrow5x\left(x+1\right)-8\left(x+1\right)=0\)

\(\Leftrightarrow\left(5x-8\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-8=0\\x+1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{8}{5}\\x=-1\end{matrix}\right.\)