(2x-8)(6x+12)=0

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Solution for (2x-8)(6x+12)=0 equation: 


Simplifying
(2x + -8)(6x + 12) = 0

Reorder the terms:
(-8 + 2x)(6x + 12) = 0

Reorder the terms:
(-8 + 2x)(12 + 6x) = 0

Multiply (-8 + 2x) * (12 + 6x)
(-8(12 + 6x) + 2x * (12 + 6x)) = 0
((12 * -8 + 6x * -8) + 2x * (12 + 6x)) = 0
((-96 + -48x) + 2x * (12 + 6x)) = 0
(-96 + -48x + (12 * 2x + 6x * 2x)) = 0
(-96 + -48x + (24x + 12x2)) = 0

Combine like terms: -48x + 24x = -24x
(-96 + -24x + 12x2) = 0

Solving
-96 + -24x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-8 + -2x + x2) = 0

Factor a trinomial.
12((-2 + -1x)(4 + -1x)) = 0

Ignore the factor 12.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 4}

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