(2x-8)(6x+4)=0

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Solution for (2x-8)(6x+4)=0 equation: 


Simplifying
(2x + -8)(6x + 4) = 0

Reorder the terms:
(-8 + 2x)(6x + 4) = 0

Reorder the terms:
(-8 + 2x)(4 + 6x) = 0

Multiply (-8 + 2x) * (4 + 6x)
(-8(4 + 6x) + 2x * (4 + 6x)) = 0
((4 * -8 + 6x * -8) + 2x * (4 + 6x)) = 0
((-32 + -48x) + 2x * (4 + 6x)) = 0
(-32 + -48x + (4 * 2x + 6x * 2x)) = 0
(-32 + -48x + (8x + 12x2)) = 0

Combine like terms: -48x + 8x = -40x
(-32 + -40x + 12x2) = 0

Solving
-32 + -40x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + -10x + 3x2) = 0

Factor a trinomial.
4((-2 + -3x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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 = {-0.6666666667, 4}

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