(4x+12)(x-6)=0

Solution for (4x+12)(x-6)=0 equation:

Simplifying
(4x + 12)(x + -6) = 0

Reorder the terms:
(12 + 4x)(x + -6) = 0

Reorder the terms:
(12 + 4x)(-6 + x) = 0

Multiply (12 + 4x) * (-6 + x)
(12(-6 + x) + 4x * (-6 + x)) = 0
((-6 * 12 + x * 12) + 4x * (-6 + x)) = 0
((-72 + 12x) + 4x * (-6 + x)) = 0
(-72 + 12x + (-6 * 4x + x * 4x)) = 0
(-72 + 12x + (-24x + 4x2)) = 0

Combine like terms: 12x + -24x = -12x
(-72 + -12x + 4x2) = 0

Solving
-72 + -12x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -3x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 6}