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

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


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

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

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

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

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

Solving
-48 + 36x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-4 + 3x + x2) = 0

Factor a trinomial.
12((-4 + -1x)(1 + -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 '(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
Solution
x = {-4, 1}

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