8(x-8)(x+1)=(x+5)(x-3)

Solution for 8(x-8)(x+1)=(x+5)(x-3) equation:

Simplifying
8(x + -8)(x + 1) = (x + 5)(x + -3)

Reorder the terms:
8(-8 + x)(x + 1) = (x + 5)(x + -3)

Reorder the terms:
8(-8 + x)(1 + x) = (x + 5)(x + -3)

Multiply (-8 + x) * (1 + x)
8(-8(1 + x) + x(1 + x)) = (x + 5)(x + -3)
8((1 * -8 + x * -8) + x(1 + x)) = (x + 5)(x + -3)
8((-8 + -8x) + x(1 + x)) = (x + 5)(x + -3)
8(-8 + -8x + (1 * x + x * x)) = (x + 5)(x + -3)
8(-8 + -8x + (1x + x2)) = (x + 5)(x + -3)

Combine like terms: -8x + 1x = -7x
8(-8 + -7x + x2) = (x + 5)(x + -3)
(-8 * 8 + -7x * 8 + x2 * 8) = (x + 5)(x + -3)
(-64 + -56x + 8x2) = (x + 5)(x + -3)

Reorder the terms:
-64 + -56x + 8x2 = (5 + x)(x + -3)

Reorder the terms:
-64 + -56x + 8x2 = (5 + x)(-3 + x)

Multiply (5 + x) * (-3 + x)
-64 + -56x + 8x2 = (5(-3 + x) + x(-3 + x))
-64 + -56x + 8x2 = ((-3 * 5 + x * 5) + x(-3 + x))
-64 + -56x + 8x2 = ((-15 + 5x) + x(-3 + x))
-64 + -56x + 8x2 = (-15 + 5x + (-3 * x + x * x))
-64 + -56x + 8x2 = (-15 + 5x + (-3x + x2))

Combine like terms: 5x + -3x = 2x
-64 + -56x + 8x2 = (-15 + 2x + x2)

Solving
-64 + -56x + 8x2 = -15 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-64 + 15 + -56x + -2x + 8x2 + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Combine like terms: -64 + 15 = -49
-49 + -56x + -2x + 8x2 + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Combine like terms: -56x + -2x = -58x
-49 + -58x + 8x2 + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Combine like terms: 8x2 + -1x2 = 7x2
-49 + -58x + 7x2 = -15 + 2x + x2 + 15 + -2x + -1x2

Reorder the terms:
-49 + -58x + 7x2 = -15 + 15 + 2x + -2x + x2 + -1x2

Combine like terms: -15 + 15 = 0
-49 + -58x + 7x2 = 0 + 2x + -2x + x2 + -1x2
-49 + -58x + 7x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-49 + -58x + 7x2 = 0 + x2 + -1x2
-49 + -58x + 7x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-49 + -58x + 7x2 = 0

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

Divide each side by '7'.
-7 + -8.285714286x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -8.285714286x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -8.285714286x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8.285714286x + x2 = 0 + 7
-8.285714286x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-8.285714286x + x2 = 7

The x term is -8.285714286x.  Take half its coefficient (-4.142857143).
Square it (17.16326531) and add it to both sides.

Add '17.16326531' to each side of the equation.
-8.285714286x + 17.16326531 + x2 = 7 + 17.16326531

Reorder the terms:
17.16326531 + -8.285714286x + x2 = 7 + 17.16326531

Combine like terms: 7 + 17.16326531 = 24.16326531
17.16326531 + -8.285714286x + x2 = 24.16326531

Factor a perfect square on the left side:
(x + -4.142857143)(x + -4.142857143) = 24.16326531

Calculate the square root of the right side: 4.915614439

Break this problem into two subproblems by setting 
(x + -4.142857143) equal to 4.915614439 and -4.915614439.

Subproblem 1
x + -4.142857143 = 4.915614439

Simplifying
x + -4.142857143 = 4.915614439

Reorder the terms:
-4.142857143 + x = 4.915614439

Solving
-4.142857143 + x = 4.915614439

Solving for variable 'x'.

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

Add '4.142857143' to each side of the equation.
-4.142857143 + 4.142857143 + x = 4.915614439 + 4.142857143

Combine like terms: -4.142857143 + 4.142857143 = 0.000000000
0.000000000 + x = 4.915614439 + 4.142857143
x = 4.915614439 + 4.142857143

Combine like terms: 4.915614439 + 4.142857143 = 9.058471582
x = 9.058471582

Simplifying
x = 9.058471582

Subproblem 2
x + -4.142857143 = -4.915614439

Simplifying
x + -4.142857143 = -4.915614439

Reorder the terms:
-4.142857143 + x = -4.915614439

Solving
-4.142857143 + x = -4.915614439

Solving for variable 'x'.

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

Add '4.142857143' to each side of the equation.
-4.142857143 + 4.142857143 + x = -4.915614439 + 4.142857143

Combine like terms: -4.142857143 + 4.142857143 = 0.000000000
0.000000000 + x = -4.915614439 + 4.142857143
x = -4.915614439 + 4.142857143

Combine like terms: -4.915614439 + 4.142857143 = -0.772757296
x = -0.772757296

Simplifying
x = -0.772757296

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.058471582, -0.772757296}