Find the Equation Given the Roots x=-8 , x=4

$x = - 8$ , $x = 4$

Step 1

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

$(x - (- 8)) (x - 4) = 0$

Step 2

Simplify.

Expand $(x + 8) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4) + 8 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 8 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 8 x + 8 \cdot - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 + 8 x + 8 \cdot - 4 = 0$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x + 8 x + 8 \cdot - 4 = 0$

Multiply $8$ by $- 4$ .

$x^{2} - 4 x + 8 x - 32 = 0$

Add $- 4 x$ and $8 x$ .

$x^{2} + 4 x - 32 = 0$