(x-6)(x+12)=0

Solution for (x-6)(x+12)=0 equation:

Simplifying
(x + -6)(x + 12) = 0

Reorder the terms:
(-6 + x)(x + 12) = 0

Reorder the terms:
(-6 + x)(12 + x) = 0

Multiply (-6 + x) * (12 + x)
(-6(12 + x) + x(12 + x)) = 0
((12 * -6 + x * -6) + x(12 + x)) = 0
((-72 + -6x) + x(12 + x)) = 0
(-72 + -6x + (12 * x + x * x)) = 0
(-72 + -6x + (12x + x2)) = 0

Combine like terms: -6x + 12x = 6x
(-72 + 6x + x2) = 0

Solving
-72 + 6x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-12, 6}