[x+4][x-12]=0

Solution for [x+4][x-12]=0 equation:

Simplifying
[x + 4][x + -12] = 0

Reorder the terms:
[4 + x][x + -12] = 0

Reorder the terms:
[4 + x][-12 + x] = 0

Multiply [4 + x] * [-12 + x]
[4[-12 + x] + x[-12 + x]] = 0
[[-12 * 4 + x * 4] + x[-12 + x]] = 0
[[-48 + 4x] + x[-12 + x]] = 0
[-48 + 4x + [-12 * x + x * x]] = 0
[-48 + 4x + [-12x + x2]] = 0

Combine like terms: 4x + -12x = -8x
[-48 + -8x + x2] = 0

Solving
-48 + -8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x)(12 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-4, 12}