8(x-8)(x+4)+4(x+2)(x-8)=32(x-16)(x-8)

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Solution for 8(x-8)(x+4)+4(x+2)(x-8)=32(x-16)(x-8) equation: 


Simplifying
8(x + -8)(x + 4) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
8(-8 + x)(x + 4) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
8(-8 + x)(4 + x) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

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

Combine like terms: -8x + 4x = -4x
8(-32 + -4x + x2) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
(-32 * 8 + -4x * 8 + x2 * 8) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
(-256 + -32x + 8x2) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
-256 + -32x + 8x2 + 4(2 + x)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
-256 + -32x + 8x2 + 4(2 + x)(-8 + x) = 32(x + -16)(x + -8)

Multiply (2 + x) * (-8 + x)
-256 + -32x + 8x2 + 4(2(-8 + x) + x(-8 + x)) = 32(x + -16)(x + -8)
-256 + -32x + 8x2 + 4((-8 * 2 + x * 2) + x(-8 + x)) = 32(x + -16)(x + -8)
-256 + -32x + 8x2 + 4((-16 + 2x) + x(-8 + x)) = 32(x + -16)(x + -8)
-256 + -32x + 8x2 + 4(-16 + 2x + (-8 * x + x * x)) = 32(x + -16)(x + -8)
-256 + -32x + 8x2 + 4(-16 + 2x + (-8x + x2)) = 32(x + -16)(x + -8)

Combine like terms: 2x + -8x = -6x
-256 + -32x + 8x2 + 4(-16 + -6x + x2) = 32(x + -16)(x + -8)
-256 + -32x + 8x2 + (-16 * 4 + -6x * 4 + x2 * 4) = 32(x + -16)(x + -8)
-256 + -32x + 8x2 + (-64 + -24x + 4x2) = 32(x + -16)(x + -8)

Reorder the terms:
-256 + -64 + -32x + -24x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: -256 + -64 = -320
-320 + -32x + -24x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: -32x + -24x = -56x
-320 + -56x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: 8x2 + 4x2 = 12x2
-320 + -56x + 12x2 = 32(x + -16)(x + -8)

Reorder the terms:
-320 + -56x + 12x2 = 32(-16 + x)(x + -8)

Reorder the terms:
-320 + -56x + 12x2 = 32(-16 + x)(-8 + x)

Multiply (-16 + x) * (-8 + x)
-320 + -56x + 12x2 = 32(-16(-8 + x) + x(-8 + x))
-320 + -56x + 12x2 = 32((-8 * -16 + x * -16) + x(-8 + x))
-320 + -56x + 12x2 = 32((128 + -16x) + x(-8 + x))
-320 + -56x + 12x2 = 32(128 + -16x + (-8 * x + x * x))
-320 + -56x + 12x2 = 32(128 + -16x + (-8x + x2))

Combine like terms: -16x + -8x = -24x
-320 + -56x + 12x2 = 32(128 + -24x + x2)
-320 + -56x + 12x2 = (128 * 32 + -24x * 32 + x2 * 32)
-320 + -56x + 12x2 = (4096 + -768x + 32x2)

Solving
-320 + -56x + 12x2 = 4096 + -768x + 32x2

Solving for variable 'x'.

Reorder the terms:
-320 + -4096 + -56x + 768x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: -320 + -4096 = -4416
-4416 + -56x + 768x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: -56x + 768x = 712x
-4416 + 712x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: 12x2 + -32x2 = -20x2
-4416 + 712x + -20x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Reorder the terms:
-4416 + 712x + -20x2 = 4096 + -4096 + -768x + 768x + 32x2 + -32x2

Combine like terms: 4096 + -4096 = 0
-4416 + 712x + -20x2 = 0 + -768x + 768x + 32x2 + -32x2
-4416 + 712x + -20x2 = -768x + 768x + 32x2 + -32x2

Combine like terms: -768x + 768x = 0
-4416 + 712x + -20x2 = 0 + 32x2 + -32x2
-4416 + 712x + -20x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-4416 + 712x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1104 + 178x + -5x2) = 0

Factor a trinomial.
4((-138 + 5x)(8 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-138 + 5x)' equal to zero and attempt to solve:

Simplifying
-138 + 5x = 0

Solving
-138 + 5x = 0

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

Add '138' to each side of the equation.
-138 + 138 + 5x = 0 + 138

Combine like terms: -138 + 138 = 0
0 + 5x = 0 + 138
5x = 0 + 138

Combine like terms: 0 + 138 = 138
5x = 138

Divide each side by '5'.
x = 27.6

Simplifying
x = 27.6

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {27.6, 8}

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