[tex]x-5=0\:or\:x+3=0[/tex]
1) If this equation in the factored form is equal to 12, then we can tell this:
[tex]\begin{gathered} (x+1)(x-3)=12 \\ x^2-2x-3=12 \\ x^2-2x-3-12=12-12 \\ x^2-2x-15=0 \\ x=\frac{-\left(-2\right)\pm\sqrt{\left(-2\right)^2-4\cdot\:1\cdot\left(-15\right)}}{2} \\ x=\frac{-\left(-2\right)\pm\:8}{2} \\ x_1=5 \\ x_2=-3 \end{gathered}[/tex]
If expanding heose parentheses and solving via quadratic formula yields 5 and -3 we can tell that using the factor zero property, this is equivalent to saying that:
[tex]\begin{gathered} (x+1)(x-3)=12 \\ x-5=0\Rightarrow x=5 \\ x+3=0\Rightarrow x=-3 \end{gathered}[/tex]
