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

Solution for (x-4)(x+8)=0 equation:

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

Reorder the terms:
(-4 + x)(x + 8) = 0

Reorder the terms:
(-4 + x)(8 + x) = 0

Multiply (-4 + x) * (8 + x)
(-4(8 + x) + x(8 + x)) = 0
((8 * -4 + x * -4) + x(8 + x)) = 0
((-32 + -4x) + x(8 + x)) = 0
(-32 + -4x + (8 * x + x * x)) = 0
(-32 + -4x + (8x + x2)) = 0

Combine like terms: -4x + 8x = 4x
(-32 + 4x + x2) = 0

Solving
-32 + 4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8, 4}