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

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

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

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

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

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

Combine like terms: 72x + 24x = 96x
(72 + 96x + 24x2) = 0

Solving
72 + 96x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(3 + 4x + x2) = 0

Factor a trinomial.
24((3 + x)(1 + x)) = 0

Ignore the factor 24.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-3, -1}