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

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


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

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

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

Multiply (-8 + x) * (-4 + 2x)
(-8(-4 + 2x) + x(-4 + 2x)) = 2(x + 6)(x + -4) + 8
((-4 * -8 + 2x * -8) + x(-4 + 2x)) = 2(x + 6)(x + -4) + 8
((32 + -16x) + x(-4 + 2x)) = 2(x + 6)(x + -4) + 8
(32 + -16x + (-4 * x + 2x * x)) = 2(x + 6)(x + -4) + 8
(32 + -16x + (-4x + 2x2)) = 2(x + 6)(x + -4) + 8

Combine like terms: -16x + -4x = -20x
(32 + -20x + 2x2) = 2(x + 6)(x + -4) + 8

Reorder the terms:
32 + -20x + 2x2 = 2(6 + x)(x + -4) + 8

Reorder the terms:
32 + -20x + 2x2 = 2(6 + x)(-4 + x) + 8

Multiply (6 + x) * (-4 + x)
32 + -20x + 2x2 = 2(6(-4 + x) + x(-4 + x)) + 8
32 + -20x + 2x2 = 2((-4 * 6 + x * 6) + x(-4 + x)) + 8
32 + -20x + 2x2 = 2((-24 + 6x) + x(-4 + x)) + 8
32 + -20x + 2x2 = 2(-24 + 6x + (-4 * x + x * x)) + 8
32 + -20x + 2x2 = 2(-24 + 6x + (-4x + x2)) + 8

Combine like terms: 6x + -4x = 2x
32 + -20x + 2x2 = 2(-24 + 2x + x2) + 8
32 + -20x + 2x2 = (-24 * 2 + 2x * 2 + x2 * 2) + 8
32 + -20x + 2x2 = (-48 + 4x + 2x2) + 8

Reorder the terms:
32 + -20x + 2x2 = -48 + 8 + 4x + 2x2

Combine like terms: -48 + 8 = -40
32 + -20x + 2x2 = -40 + 4x + 2x2

Add '-2x2' to each side of the equation.
32 + -20x + 2x2 + -2x2 = -40 + 4x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
32 + -20x + 0 = -40 + 4x + 2x2 + -2x2
32 + -20x = -40 + 4x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
32 + -20x = -40 + 4x + 0
32 + -20x = -40 + 4x

Solving
32 + -20x = -40 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
32 + -20x + -4x = -40 + 4x + -4x

Combine like terms: -20x + -4x = -24x
32 + -24x = -40 + 4x + -4x

Combine like terms: 4x + -4x = 0
32 + -24x = -40 + 0
32 + -24x = -40

Add '-32' to each side of the equation.
32 + -32 + -24x = -40 + -32

Combine like terms: 32 + -32 = 0
0 + -24x = -40 + -32
-24x = -40 + -32

Combine like terms: -40 + -32 = -72
-24x = -72

Divide each side by '-24'.
x = 3

Simplifying
x = 3

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