8(x-5)(x+10)+4(x+2)(x-8)=32(x-16)(x-4)

Solution for 8(x-5)(x+10)+4(x+2)(x-8)=32(x-16)(x-4) equation:

Simplifying
8(x + -5)(x + 10) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)

Reorder the terms:
8(-5 + x)(x + 10) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)

Reorder the terms:
8(-5 + x)(10 + x) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)

Multiply (-5 + x) * (10 + x)
8(-5(10 + x) + x(10 + x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)
8((10 * -5 + x * -5) + x(10 + x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)
8((-50 + -5x) + x(10 + x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)
8(-50 + -5x + (10 * x + x * x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)
8(-50 + -5x + (10x + x2)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)

Combine like terms: -5x + 10x = 5x
8(-50 + 5x + x2) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)
(-50 * 8 + 5x * 8 + x2 * 8) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)
(-400 + 40x + 8x2) + 4(x + 2)(x + -8) = 32(x + -16)(x + -4)

Reorder the terms:
-400 + 40x + 8x2 + 4(2 + x)(x + -8) = 32(x + -16)(x + -4)

Reorder the terms:
-400 + 40x + 8x2 + 4(2 + x)(-8 + x) = 32(x + -16)(x + -4)

Multiply (2 + x) * (-8 + x)
-400 + 40x + 8x2 + 4(2(-8 + x) + x(-8 + x)) = 32(x + -16)(x + -4)
-400 + 40x + 8x2 + 4((-8 * 2 + x * 2) + x(-8 + x)) = 32(x + -16)(x + -4)
-400 + 40x + 8x2 + 4((-16 + 2x) + x(-8 + x)) = 32(x + -16)(x + -4)
-400 + 40x + 8x2 + 4(-16 + 2x + (-8 * x + x * x)) = 32(x + -16)(x + -4)
-400 + 40x + 8x2 + 4(-16 + 2x + (-8x + x2)) = 32(x + -16)(x + -4)

Combine like terms: 2x + -8x = -6x
-400 + 40x + 8x2 + 4(-16 + -6x + x2) = 32(x + -16)(x + -4)
-400 + 40x + 8x2 + (-16 * 4 + -6x * 4 + x2 * 4) = 32(x + -16)(x + -4)
-400 + 40x + 8x2 + (-64 + -24x + 4x2) = 32(x + -16)(x + -4)

Reorder the terms:
-400 + -64 + 40x + -24x + 8x2 + 4x2 = 32(x + -16)(x + -4)

Combine like terms: -400 + -64 = -464
-464 + 40x + -24x + 8x2 + 4x2 = 32(x + -16)(x + -4)

Combine like terms: 40x + -24x = 16x
-464 + 16x + 8x2 + 4x2 = 32(x + -16)(x + -4)

Combine like terms: 8x2 + 4x2 = 12x2
-464 + 16x + 12x2 = 32(x + -16)(x + -4)

Reorder the terms:
-464 + 16x + 12x2 = 32(-16 + x)(x + -4)

Reorder the terms:
-464 + 16x + 12x2 = 32(-16 + x)(-4 + x)

Multiply (-16 + x) * (-4 + x)
-464 + 16x + 12x2 = 32(-16(-4 + x) + x(-4 + x))
-464 + 16x + 12x2 = 32((-4 * -16 + x * -16) + x(-4 + x))
-464 + 16x + 12x2 = 32((64 + -16x) + x(-4 + x))
-464 + 16x + 12x2 = 32(64 + -16x + (-4 * x + x * x))
-464 + 16x + 12x2 = 32(64 + -16x + (-4x + x2))

Combine like terms: -16x + -4x = -20x
-464 + 16x + 12x2 = 32(64 + -20x + x2)
-464 + 16x + 12x2 = (64 * 32 + -20x * 32 + x2 * 32)
-464 + 16x + 12x2 = (2048 + -640x + 32x2)

Solving
-464 + 16x + 12x2 = 2048 + -640x + 32x2

Solving for variable 'x'.

Reorder the terms:
-464 + -2048 + 16x + 640x + 12x2 + -32x2 = 2048 + -640x + 32x2 + -2048 + 640x + -32x2

Combine like terms: -464 + -2048 = -2512
-2512 + 16x + 640x + 12x2 + -32x2 = 2048 + -640x + 32x2 + -2048 + 640x + -32x2

Combine like terms: 16x + 640x = 656x
-2512 + 656x + 12x2 + -32x2 = 2048 + -640x + 32x2 + -2048 + 640x + -32x2

Combine like terms: 12x2 + -32x2 = -20x2
-2512 + 656x + -20x2 = 2048 + -640x + 32x2 + -2048 + 640x + -32x2

Reorder the terms:
-2512 + 656x + -20x2 = 2048 + -2048 + -640x + 640x + 32x2 + -32x2

Combine like terms: 2048 + -2048 = 0
-2512 + 656x + -20x2 = 0 + -640x + 640x + 32x2 + -32x2
-2512 + 656x + -20x2 = -640x + 640x + 32x2 + -32x2

Combine like terms: -640x + 640x = 0
-2512 + 656x + -20x2 = 0 + 32x2 + -32x2
-2512 + 656x + -20x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-2512 + 656x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-628 + 164x + -5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-628 + 164x + -5x2)' equal to zero and attempt to solve:

Simplifying
-628 + 164x + -5x2 = 0

Solving
-628 + 164x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
125.6 + -32.8x + x2 = 0

Move the constant term to the right:

Add '-125.6' to each side of the equation.
125.6 + -32.8x + -125.6 + x2 = 0 + -125.6

Reorder the terms:
125.6 + -125.6 + -32.8x + x2 = 0 + -125.6

Combine like terms: 125.6 + -125.6 = 0.0
0.0 + -32.8x + x2 = 0 + -125.6
-32.8x + x2 = 0 + -125.6

Combine like terms: 0 + -125.6 = -125.6
-32.8x + x2 = -125.6

The x term is -32.8x.  Take half its coefficient (-16.4).
Square it (268.96) and add it to both sides.

Add '268.96' to each side of the equation.
-32.8x + 268.96 + x2 = -125.6 + 268.96

Reorder the terms:
268.96 + -32.8x + x2 = -125.6 + 268.96

Combine like terms: -125.6 + 268.96 = 143.36
268.96 + -32.8x + x2 = 143.36

Factor a perfect square on the left side:
(x + -16.4)(x + -16.4) = 143.36

Calculate the square root of the right side: 11.973303638

Break this problem into two subproblems by setting 
(x + -16.4) equal to 11.973303638 and -11.973303638.

Subproblem 1
x + -16.4 = 11.973303638

Simplifying
x + -16.4 = 11.973303638

Reorder the terms:
-16.4 + x = 11.973303638

Solving
-16.4 + x = 11.973303638

Solving for variable 'x'.

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

Add '16.4' to each side of the equation.
-16.4 + 16.4 + x = 11.973303638 + 16.4

Combine like terms: -16.4 + 16.4 = 0.0
0.0 + x = 11.973303638 + 16.4
x = 11.973303638 + 16.4

Combine like terms: 11.973303638 + 16.4 = 28.373303638
x = 28.373303638

Simplifying
x = 28.373303638

Subproblem 2
x + -16.4 = -11.973303638

Simplifying
x + -16.4 = -11.973303638

Reorder the terms:
-16.4 + x = -11.973303638

Solving
-16.4 + x = -11.973303638

Solving for variable 'x'.

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

Add '16.4' to each side of the equation.
-16.4 + 16.4 + x = -11.973303638 + 16.4

Combine like terms: -16.4 + 16.4 = 0.0
0.0 + x = -11.973303638 + 16.4
x = -11.973303638 + 16.4

Combine like terms: -11.973303638 + 16.4 = 4.426696362
x = 4.426696362

Simplifying
x = 4.426696362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.373303638, 4.426696362}
Solution
x = {28.373303638, 4.426696362}