(3x+3)(4x-12)=0

Solution for (3x+3)(4x-12)=0 equation:

Simplifying
(3x + 3)(4x + -12) = 0

Reorder the terms:
(3 + 3x)(4x + -12) = 0

Reorder the terms:
(3 + 3x)(-12 + 4x) = 0

Multiply (3 + 3x) * (-12 + 4x)
(3(-12 + 4x) + 3x * (-12 + 4x)) = 0
((-12 * 3 + 4x * 3) + 3x * (-12 + 4x)) = 0
((-36 + 12x) + 3x * (-12 + 4x)) = 0
(-36 + 12x + (-12 * 3x + 4x * 3x)) = 0
(-36 + 12x + (-36x + 12x2)) = 0

Combine like terms: 12x + -36x = -24x
(-36 + -24x + 12x2) = 0

Solving
-36 + -24x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + -2x + x2) = 0

Factor a trinomial.
12((-1 + -1x)(3 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 3}