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

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


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

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

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

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

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

Solving
-144 + 12x + 12x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 12.

Subproblem 1
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

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 = {-4, 3}

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