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

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


Simplifying
2(x + -4) * 4x + -1(x + -2) * 2x = (x + -8) * 8x

Reorder the terms:
2(-4 + x) * 4x + -1(x + -2) * 2x = (x + -8) * 8x

Reorder the terms for easier multiplication:
2 * 4x(-4 + x) + -1(x + -2) * 2x = (x + -8) * 8x

Multiply 2 * 4
8x(-4 + x) + -1(x + -2) * 2x = (x + -8) * 8x
(-4 * 8x + x * 8x) + -1(x + -2) * 2x = (x + -8) * 8x
(-32x + 8x2) + -1(x + -2) * 2x = (x + -8) * 8x

Reorder the terms:
-32x + 8x2 + -1(-2 + x) * 2x = (x + -8) * 8x

Reorder the terms for easier multiplication:
-32x + 8x2 + -1 * 2x(-2 + x) = (x + -8) * 8x

Multiply -1 * 2
-32x + 8x2 + -2x(-2 + x) = (x + -8) * 8x
-32x + 8x2 + (-2 * -2x + x * -2x) = (x + -8) * 8x
-32x + 8x2 + (4x + -2x2) = (x + -8) * 8x

Reorder the terms:
-32x + 4x + 8x2 + -2x2 = (x + -8) * 8x

Combine like terms: -32x + 4x = -28x
-28x + 8x2 + -2x2 = (x + -8) * 8x

Combine like terms: 8x2 + -2x2 = 6x2
-28x + 6x2 = (x + -8) * 8x

Reorder the terms:
-28x + 6x2 = (-8 + x) * 8x

Reorder the terms for easier multiplication:
-28x + 6x2 = 8x(-8 + x)
-28x + 6x2 = (-8 * 8x + x * 8x)
-28x + 6x2 = (-64x + 8x2)

Solving
-28x + 6x2 = -64x + 8x2

Solving for variable 'x'.

Reorder the terms:
-28x + 64x + 6x2 + -8x2 = -64x + 8x2 + 64x + -8x2

Combine like terms: -28x + 64x = 36x
36x + 6x2 + -8x2 = -64x + 8x2 + 64x + -8x2

Combine like terms: 6x2 + -8x2 = -2x2
36x + -2x2 = -64x + 8x2 + 64x + -8x2

Reorder the terms:
36x + -2x2 = -64x + 64x + 8x2 + -8x2

Combine like terms: -64x + 64x = 0
36x + -2x2 = 0 + 8x2 + -8x2
36x + -2x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
36x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(18 + -1x) = 0

Ignore the factor 2.

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 '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {0, 18}

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