(x^2-8x+16)(2x-8)-(x^2-8x+12)(2(x-4))=0

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Solution for (x^2-8x+16)(2x-8)-(x^2-8x+12)(2(x-4))=0 equation: 


Simplifying
(x2 + -8x + 16)(2x + -8) + -1(x2 + -8x + 12)(2(x + -4)) = 0

Reorder the terms:
(16 + -8x + x2)(2x + -8) + -1(x2 + -8x + 12)(2(x + -4)) = 0

Reorder the terms:
(16 + -8x + x2)(-8 + 2x) + -1(x2 + -8x + 12)(2(x + -4)) = 0

Multiply (16 + -8x + x2) * (-8 + 2x)
(16(-8 + 2x) + -8x * (-8 + 2x) + x2(-8 + 2x)) + -1(x2 + -8x + 12)(2(x + -4)) = 0
((-8 * 16 + 2x * 16) + -8x * (-8 + 2x) + x2(-8 + 2x)) + -1(x2 + -8x + 12)(2(x + -4)) = 0
((-128 + 32x) + -8x * (-8 + 2x) + x2(-8 + 2x)) + -1(x2 + -8x + 12)(2(x + -4)) = 0
(-128 + 32x + (-8 * -8x + 2x * -8x) + x2(-8 + 2x)) + -1(x2 + -8x + 12)(2(x + -4)) = 0
(-128 + 32x + (64x + -16x2) + x2(-8 + 2x)) + -1(x2 + -8x + 12)(2(x + -4)) = 0
(-128 + 32x + 64x + -16x2 + (-8 * x2 + 2x * x2)) + -1(x2 + -8x + 12)(2(x + -4)) = 0
(-128 + 32x + 64x + -16x2 + (-8x2 + 2x3)) + -1(x2 + -8x + 12)(2(x + -4)) = 0

Combine like terms: 32x + 64x = 96x
(-128 + 96x + -16x2 + -8x2 + 2x3) + -1(x2 + -8x + 12)(2(x + -4)) = 0

Combine like terms: -16x2 + -8x2 = -24x2
(-128 + 96x + -24x2 + 2x3) + -1(x2 + -8x + 12)(2(x + -4)) = 0

Reorder the terms:
-128 + 96x + -24x2 + 2x3 + -1(12 + -8x + x2)(2(x + -4)) = 0

Reorder the terms:
-128 + 96x + -24x2 + 2x3 + -1(12 + -8x + x2)(2(-4 + x)) = 0
-128 + 96x + -24x2 + 2x3 + -1(12 + -8x + x2)((-4 * 2 + x * 2)) = 0
-128 + 96x + -24x2 + 2x3 + -1(12 + -8x + x2)((-8 + 2x)) = 0

Multiply (12 + -8x + x2) * (-8 + 2x)
-128 + 96x + -24x2 + 2x3 + -1(12(-8 + 2x) + -8x * (-8 + 2x) + x2(-8 + 2x)) = 0
-128 + 96x + -24x2 + 2x3 + -1((-8 * 12 + 2x * 12) + -8x * (-8 + 2x) + x2(-8 + 2x)) = 0
-128 + 96x + -24x2 + 2x3 + -1((-96 + 24x) + -8x * (-8 + 2x) + x2(-8 + 2x)) = 0
-128 + 96x + -24x2 + 2x3 + -1(-96 + 24x + (-8 * -8x + 2x * -8x) + x2(-8 + 2x)) = 0
-128 + 96x + -24x2 + 2x3 + -1(-96 + 24x + (64x + -16x2) + x2(-8 + 2x)) = 0
-128 + 96x + -24x2 + 2x3 + -1(-96 + 24x + 64x + -16x2 + (-8 * x2 + 2x * x2)) = 0
-128 + 96x + -24x2 + 2x3 + -1(-96 + 24x + 64x + -16x2 + (-8x2 + 2x3)) = 0

Combine like terms: 24x + 64x = 88x
-128 + 96x + -24x2 + 2x3 + -1(-96 + 88x + -16x2 + -8x2 + 2x3) = 0

Combine like terms: -16x2 + -8x2 = -24x2
-128 + 96x + -24x2 + 2x3 + -1(-96 + 88x + -24x2 + 2x3) = 0
-128 + 96x + -24x2 + 2x3 + (-96 * -1 + 88x * -1 + -24x2 * -1 + 2x3 * -1) = 0
-128 + 96x + -24x2 + 2x3 + (96 + -88x + 24x2 + -2x3) = 0

Reorder the terms:
-128 + 96 + 96x + -88x + -24x2 + 24x2 + 2x3 + -2x3 = 0

Combine like terms: -128 + 96 = -32
-32 + 96x + -88x + -24x2 + 24x2 + 2x3 + -2x3 = 0

Combine like terms: 96x + -88x = 8x
-32 + 8x + -24x2 + 24x2 + 2x3 + -2x3 = 0

Combine like terms: -24x2 + 24x2 = 0
-32 + 8x + 0 + 2x3 + -2x3 = 0
-32 + 8x + 2x3 + -2x3 = 0

Combine like terms: 2x3 + -2x3 = 0
-32 + 8x + 0 = 0
-32 + 8x = 0

Solving
-32 + 8x = 0

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + 8x = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 8x = 0 + 32
8x = 0 + 32

Combine like terms: 0 + 32 = 32
8x = 32

Divide each side by '8'.
x = 4

Simplifying
x = 4

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