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

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


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

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

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

Multiply (-12 + 3x) * (12 + 4x)
(-12(12 + 4x) + 3x * (12 + 4x)) = 0
((12 * -12 + 4x * -12) + 3x * (12 + 4x)) = 0
((-144 + -48x) + 3x * (12 + 4x)) = 0
(-144 + -48x + (12 * 3x + 4x * 3x)) = 0
(-144 + -48x + (36x + 12x2)) = 0

Combine like terms: -48x + 36x = -12x
(-144 + -12x + 12x2) = 0

Solving
-144 + -12x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-12 + -1x + x2) = 0

Factor a trinomial.
12((-3 + -1x)(4 + -1x)) = 0

Ignore the factor 12.

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 '(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
Solution
x = {-3, 4}

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