8(x-6)(x+10)+4(x+2)(x-14)=32(x-16)(x-8)

Solution for 8(x-6)(x+10)+4(x+2)(x-14)=32(x-16)(x-8) equation:

Simplifying
8(x + -6)(x + 10) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)

Reorder the terms:
8(-6 + x)(x + 10) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)

Reorder the terms:
8(-6 + x)(10 + x) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)

Multiply (-6 + x) * (10 + x)
8(-6(10 + x) + x(10 + x)) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)
8((10 * -6 + x * -6) + x(10 + x)) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)
8((-60 + -6x) + x(10 + x)) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)
8(-60 + -6x + (10 * x + x * x)) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)
8(-60 + -6x + (10x + x2)) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)

Combine like terms: -6x + 10x = 4x
8(-60 + 4x + x2) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)
(-60 * 8 + 4x * 8 + x2 * 8) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)
(-480 + 32x + 8x2) + 4(x + 2)(x + -14) = 32(x + -16)(x + -8)

Reorder the terms:
-480 + 32x + 8x2 + 4(2 + x)(x + -14) = 32(x + -16)(x + -8)

Reorder the terms:
-480 + 32x + 8x2 + 4(2 + x)(-14 + x) = 32(x + -16)(x + -8)

Multiply (2 + x) * (-14 + x)
-480 + 32x + 8x2 + 4(2(-14 + x) + x(-14 + x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4((-14 * 2 + x * 2) + x(-14 + x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4((-28 + 2x) + x(-14 + x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4(-28 + 2x + (-14 * x + x * x)) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + 4(-28 + 2x + (-14x + x2)) = 32(x + -16)(x + -8)

Combine like terms: 2x + -14x = -12x
-480 + 32x + 8x2 + 4(-28 + -12x + x2) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + (-28 * 4 + -12x * 4 + x2 * 4) = 32(x + -16)(x + -8)
-480 + 32x + 8x2 + (-112 + -48x + 4x2) = 32(x + -16)(x + -8)

Reorder the terms:
-480 + -112 + 32x + -48x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: -480 + -112 = -592
-592 + 32x + -48x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: 32x + -48x = -16x
-592 + -16x + 8x2 + 4x2 = 32(x + -16)(x + -8)

Combine like terms: 8x2 + 4x2 = 12x2
-592 + -16x + 12x2 = 32(x + -16)(x + -8)

Reorder the terms:
-592 + -16x + 12x2 = 32(-16 + x)(x + -8)

Reorder the terms:
-592 + -16x + 12x2 = 32(-16 + x)(-8 + x)

Multiply (-16 + x) * (-8 + x)
-592 + -16x + 12x2 = 32(-16(-8 + x) + x(-8 + x))
-592 + -16x + 12x2 = 32((-8 * -16 + x * -16) + x(-8 + x))
-592 + -16x + 12x2 = 32((128 + -16x) + x(-8 + x))
-592 + -16x + 12x2 = 32(128 + -16x + (-8 * x + x * x))
-592 + -16x + 12x2 = 32(128 + -16x + (-8x + x2))

Combine like terms: -16x + -8x = -24x
-592 + -16x + 12x2 = 32(128 + -24x + x2)
-592 + -16x + 12x2 = (128 * 32 + -24x * 32 + x2 * 32)
-592 + -16x + 12x2 = (4096 + -768x + 32x2)

Solving
-592 + -16x + 12x2 = 4096 + -768x + 32x2

Solving for variable 'x'.

Reorder the terms:
-592 + -4096 + -16x + 768x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: -592 + -4096 = -4688
-4688 + -16x + 768x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: -16x + 768x = 752x
-4688 + 752x + 12x2 + -32x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Combine like terms: 12x2 + -32x2 = -20x2
-4688 + 752x + -20x2 = 4096 + -768x + 32x2 + -4096 + 768x + -32x2

Reorder the terms:
-4688 + 752x + -20x2 = 4096 + -4096 + -768x + 768x + 32x2 + -32x2

Combine like terms: 4096 + -4096 = 0
-4688 + 752x + -20x2 = 0 + -768x + 768x + 32x2 + -32x2
-4688 + 752x + -20x2 = -768x + 768x + 32x2 + -32x2

Combine like terms: -768x + 768x = 0
-4688 + 752x + -20x2 = 0 + 32x2 + -32x2
-4688 + 752x + -20x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-4688 + 752x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1172 + 188x + -5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1172 + 188x + -5x2)' equal to zero and attempt to solve:

Simplifying
-1172 + 188x + -5x2 = 0

Solving
-1172 + 188x + -5x2 = 0

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

Divide each side by '-5'.
234.4 + -37.6x + x2 = 0

Move the constant term to the right:

Add '-234.4' to each side of the equation.
234.4 + -37.6x + -234.4 + x2 = 0 + -234.4

Reorder the terms:
234.4 + -234.4 + -37.6x + x2 = 0 + -234.4

Combine like terms: 234.4 + -234.4 = 0.0
0.0 + -37.6x + x2 = 0 + -234.4
-37.6x + x2 = 0 + -234.4

Combine like terms: 0 + -234.4 = -234.4
-37.6x + x2 = -234.4

The x term is -37.6x.  Take half its coefficient (-18.8).
Square it (353.44) and add it to both sides.

Add '353.44' to each side of the equation.
-37.6x + 353.44 + x2 = -234.4 + 353.44

Reorder the terms:
353.44 + -37.6x + x2 = -234.4 + 353.44

Combine like terms: -234.4 + 353.44 = 119.04
353.44 + -37.6x + x2 = 119.04

Factor a perfect square on the left side:
(x + -18.8)(x + -18.8) = 119.04

Calculate the square root of the right side: 10.910545358

Break this problem into two subproblems by setting 
(x + -18.8) equal to 10.910545358 and -10.910545358.

Subproblem 1
x + -18.8 = 10.910545358

Simplifying
x + -18.8 = 10.910545358

Reorder the terms:
-18.8 + x = 10.910545358

Solving
-18.8 + x = 10.910545358

Solving for variable 'x'.

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

Add '18.8' to each side of the equation.
-18.8 + 18.8 + x = 10.910545358 + 18.8

Combine like terms: -18.8 + 18.8 = 0.0
0.0 + x = 10.910545358 + 18.8
x = 10.910545358 + 18.8

Combine like terms: 10.910545358 + 18.8 = 29.710545358
x = 29.710545358

Simplifying
x = 29.710545358

Subproblem 2
x + -18.8 = -10.910545358

Simplifying
x + -18.8 = -10.910545358

Reorder the terms:
-18.8 + x = -10.910545358

Solving
-18.8 + x = -10.910545358

Solving for variable 'x'.

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

Add '18.8' to each side of the equation.
-18.8 + 18.8 + x = -10.910545358 + 18.8

Combine like terms: -18.8 + 18.8 = 0.0
0.0 + x = -10.910545358 + 18.8
x = -10.910545358 + 18.8

Combine like terms: -10.910545358 + 18.8 = 7.889454642
x = 7.889454642

Simplifying
x = 7.889454642

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.710545358, 7.889454642}
Solution
x = {29.710545358, 7.889454642}