(2(x-2)-4)(3x(2x-8))=0

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Solution for (2(x-2)-4)(3x(2x-8))=0 equation: 


Simplifying
(2(x + -2) + -4)(3x(2x + -8)) = 0

Reorder the terms:
(2(-2 + x) + -4)(3x(2x + -8)) = 0
((-2 * 2 + x * 2) + -4)(3x(2x + -8)) = 0
((-4 + 2x) + -4)(3x(2x + -8)) = 0

Reorder the terms:
(-4 + -4 + 2x)(3x(2x + -8)) = 0

Combine like terms: -4 + -4 = -8
(-8 + 2x)(3x(2x + -8)) = 0

Reorder the terms:
(-8 + 2x)(3x(-8 + 2x)) = 0
(-8 + 2x)((-8 * 3x + 2x * 3x)) = 0
(-8 + 2x)((-24x + 6x2)) = 0

Multiply (-8 + 2x) * (-24x + 6x2)
(-8(-24x + 6x2) + 2x * (-24x + 6x2)) = 0
((-24x * -8 + 6x2 * -8) + 2x * (-24x + 6x2)) = 0
((192x + -48x2) + 2x * (-24x + 6x2)) = 0
(192x + -48x2 + (-24x * 2x + 6x2 * 2x)) = 0
(192x + -48x2 + (-48x2 + 12x3)) = 0

Combine like terms: -48x2 + -48x2 = -96x2
(192x + -96x2 + 12x3) = 0

Solving
192x + -96x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(16 + -8x + x2) = 0

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

Ignore the factor 12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Subproblem 3
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, 4, 4}

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