(2x-8)(4x-64)=0

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Solution for (2x-8)(4x-64)=0 equation: 


Simplifying
(2x + -8)(4x + -64) = 0

Reorder the terms:
(-8 + 2x)(4x + -64) = 0

Reorder the terms:
(-8 + 2x)(-64 + 4x) = 0

Multiply (-8 + 2x) * (-64 + 4x)
(-8(-64 + 4x) + 2x * (-64 + 4x)) = 0
((-64 * -8 + 4x * -8) + 2x * (-64 + 4x)) = 0
((512 + -32x) + 2x * (-64 + 4x)) = 0
(512 + -32x + (-64 * 2x + 4x * 2x)) = 0
(512 + -32x + (-128x + 8x2)) = 0

Combine like terms: -32x + -128x = -160x
(512 + -160x + 8x2) = 0

Solving
512 + -160x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(64 + -20x + x2) = 0

Factor a trinomial.
8((4 + -1x)(16 + -1x)) = 0

Ignore the factor 8.

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 '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {4, 16}

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