8(x-6)(x+10)+4(x+2)(x-8)=32(x-16)(x-8)

Solution for 8(x-6)(x+10)+4(x+2)(x-8)=32(x-16)(x-8) equation:

Simplifying
8(x + -6)(x + 10) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
8(-6 + x)(x + 10) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
8(-6 + x)(10 + x) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Multiply (-6 + x) * (10 + x)
8(-6(10 + x) + x(10 + x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
8((10 * -6 + x * -6) + x(10 + x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
8((-60 + -6x) + x(10 + x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
8(-60 + -6x + (10 * x + x * x)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
8(-60 + -6x + (10x + x2)) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Combine like terms: -6x + 10x = 4x
8(-60 + 4x + x2) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
(-60 * 8 + 4x * 8 + x2 * 8) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)
(-480 + 32x + 8x2) + 4(x + 2)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
-480 + 32x + 8x2 + 4(2 + x)(x + -8) = 32(x + -16)(x + -8)

Reorder the terms:
-480 + 32x + 8x2 + 4(2 + x)(-8 + x) = 32(x + -16)(x + -8)

Multiply (2 + x) * (-8 + x)
-480 + 32x + 8x2 + 4(2(-8 + x) + x(-8 + x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4((-8 * 2 + x * 2) + x(-8 + x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4((-16 + 2x) + x(-8 + x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4(-16 + 2x + (-8 * x + x * x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4(-16 + 2x + (-8x + x2)) = 32(x + -16)(x + -8)

Combine like terms: 2x + -8x = -6x
-480 + 32x + 8x2 + 4(-16 + -6x + x2) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + (-16 * 4 + -6x * 4 + x2 * 4) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + (-64 + -24x + 4x2) = 32(x + -16)(x + -8)

Reorder the terms:
-480 + -64 + 32x + -24x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: -480 + -64 = -544
-544 + 32x + -24x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: 32x + -24x = 8x
-544 + 8x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: 8x2 + 4x2 = 12x2
-544 + 8x + 12x2 = 32(x + -16)(x + -8)

Reorder the terms:
-544 + 8x + 12x2 = 32(-16 + x)(x + -8)

Reorder the terms:
-544 + 8x + 12x2 = 32(-16 + x)(-8 + x)

Multiply (-16 + x) * (-8 + x)
-544 + 8x + 12x2 = 32(-16(-8 + x) + x(-8 + x))
-544 + 8x + 12x2 = 32((-8 * -16 + x * -16) + x(-8 + x))
-544 + 8x + 12x2 = 32((128 + -16x) + x(-8 + x))
-544 + 8x + 12x2 = 32(128 + -16x + (-8 * x + x * x))
-544 + 8x + 12x2 = 32(128 + -16x + (-8x + x2))

Combine like terms: -16x + -8x = -24x
-544 + 8x + 12x2 = 32(128 + -24x + x2)
-544 + 8x + 12x2 = (128 * 32 + -24x * 32 + x2 * 32)
-544 + 8x + 12x2 = (4096 + -768x + 32x2)

Solving
-544 + 8x + 12x2 = 4096 + -768x + 32x2

Solving for variable 'x'.

Reorder the terms:
-544 + -4096 + 8x + 768x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: -544 + -4096 = -4640
-4640 + 8x + 768x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: 8x + 768x = 776x
-4640 + 776x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: 12x2 + -32x2 = -20x2
-4640 + 776x + -20x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Reorder the terms:
-4640 + 776x + -20x2 = 4096 + -4096 + -768x + 768x + 32x2 + -32x2

Combine like terms: 4096 + -4096 = 0
-4640 + 776x + -20x2 = 0 + -768x + 768x + 32x2 + -32x2
-4640 + 776x + -20x2 = -768x + 768x + 32x2 + -32x2

Combine like terms: -768x + 768x = 0
-4640 + 776x + -20x2 = 0 + 32x2 + -32x2
-4640 + 776x + -20x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-4640 + 776x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1160 + 194x + -5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1160 + 194x + -5x2)' equal to zero and attempt to solve:

Simplifying
-1160 + 194x + -5x2 = 0

Solving
-1160 + 194x + -5x2 = 0

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

Divide each side by '-5'.
232 + -38.8x + x2 = 0

Move the constant term to the right:

Add '-232' to each side of the equation.
232 + -38.8x + -232 + x2 = 0 + -232

Reorder the terms:
232 + -232 + -38.8x + x2 = 0 + -232

Combine like terms: 232 + -232 = 0
0 + -38.8x + x2 = 0 + -232
-38.8x + x2 = 0 + -232

Combine like terms: 0 + -232 = -232
-38.8x + x2 = -232

The x term is -38.8x.  Take half its coefficient (-19.4).
Square it (376.36) and add it to both sides.

Add '376.36' to each side of the equation.
-38.8x + 376.36 + x2 = -232 + 376.36

Reorder the terms:
376.36 + -38.8x + x2 = -232 + 376.36

Combine like terms: -232 + 376.36 = 144.36
376.36 + -38.8x + x2 = 144.36

Factor a perfect square on the left side:
(x + -19.4)(x + -19.4) = 144.36

Calculate the square root of the right side: 12.014990637

Break this problem into two subproblems by setting 
(x + -19.4) equal to 12.014990637 and -12.014990637.

Subproblem 1
x + -19.4 = 12.014990637

Simplifying
x + -19.4 = 12.014990637

Reorder the terms:
-19.4 + x = 12.014990637

Solving
-19.4 + x = 12.014990637

Solving for variable 'x'.

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

Add '19.4' to each side of the equation.
-19.4 + 19.4 + x = 12.014990637 + 19.4

Combine like terms: -19.4 + 19.4 = 0.0
0.0 + x = 12.014990637 + 19.4
x = 12.014990637 + 19.4

Combine like terms: 12.014990637 + 19.4 = 31.414990637
x = 31.414990637

Simplifying
x = 31.414990637

Subproblem 2
x + -19.4 = -12.014990637

Simplifying
x + -19.4 = -12.014990637

Reorder the terms:
-19.4 + x = -12.014990637

Solving
-19.4 + x = -12.014990637

Solving for variable 'x'.

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

Add '19.4' to each side of the equation.
-19.4 + 19.4 + x = -12.014990637 + 19.4

Combine like terms: -19.4 + 19.4 = 0.0
0.0 + x = -12.014990637 + 19.4
x = -12.014990637 + 19.4

Combine like terms: -12.014990637 + 19.4 = 7.385009363
x = 7.385009363

Simplifying
x = 7.385009363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.414990637, 7.385009363}
Solution
x = {31.414990637, 7.385009363}