Answer :
To use the FOIL method, we need to multiply the following terms of each factor:
Firsts: x and x
Outsiders: x and 2
Inner: -4 and x
Lasts: -4 and 2
Multiplying each pair of values and adding the results, we have:
[tex]\begin{gathered} (x-4)(x+2)\\ \\ =x\cdot x+x\operatorname{\cdot}2+(-4)\operatorname{\cdot}x+(-4)\operatorname{\cdot}2\\ \\ =x^2+2x-4x-8\\ \\ =x^2-2x-8 \end{gathered}[/tex]The equation in the standard form is y = x² - 2x - 8, and the coefficients are a = 1, b = -2 and c = -8.
Now, to solve the equation, we need to use the quadratic formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{2\pm\sqrt{4+32}}{2}\\ \\ x_1=\frac{2+6}{2}=\frac{8}{2}=4\\ \\ x_2=\frac{2-6}{2}=-\frac{4}{2}=-2 \end{gathered}[/tex]Therefore the solution is x = -2 and x = 4.