(2x+8)(3x-6)=0

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Solution for (2x+8)(3x-6)=0 equation: 


Simplifying
(2x + 8)(3x + -6) = 0

Reorder the terms:
(8 + 2x)(3x + -6) = 0

Reorder the terms:
(8 + 2x)(-6 + 3x) = 0

Multiply (8 + 2x) * (-6 + 3x)
(8(-6 + 3x) + 2x * (-6 + 3x)) = 0
((-6 * 8 + 3x * 8) + 2x * (-6 + 3x)) = 0
((-48 + 24x) + 2x * (-6 + 3x)) = 0
(-48 + 24x + (-6 * 2x + 3x * 2x)) = 0
(-48 + 24x + (-12x + 6x2)) = 0

Combine like terms: 24x + -12x = 12x
(-48 + 12x + 6x2) = 0

Solving
-48 + 12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + 2x + x2) = 0

Factor a trinomial.
6((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 6.

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 '(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
Solution
x = {-4, 2}

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