(x-8)(5x+6)=(x-10)(x-2)

Solution for (x-8)(5x+6)=(x-10)(x-2) equation:

Simplifying
(x + -8)(5x + 6) = (x + -10)(x + -2)

Reorder the terms:
(-8 + x)(5x + 6) = (x + -10)(x + -2)

Reorder the terms:
(-8 + x)(6 + 5x) = (x + -10)(x + -2)

Multiply (-8 + x) * (6 + 5x)
(-8(6 + 5x) + x(6 + 5x)) = (x + -10)(x + -2)
((6 * -8 + 5x * -8) + x(6 + 5x)) = (x + -10)(x + -2)
((-48 + -40x) + x(6 + 5x)) = (x + -10)(x + -2)
(-48 + -40x + (6 * x + 5x * x)) = (x + -10)(x + -2)
(-48 + -40x + (6x + 5x2)) = (x + -10)(x + -2)

Combine like terms: -40x + 6x = -34x
(-48 + -34x + 5x2) = (x + -10)(x + -2)

Reorder the terms:
-48 + -34x + 5x2 = (-10 + x)(x + -2)

Reorder the terms:
-48 + -34x + 5x2 = (-10 + x)(-2 + x)

Multiply (-10 + x) * (-2 + x)
-48 + -34x + 5x2 = (-10(-2 + x) + x(-2 + x))
-48 + -34x + 5x2 = ((-2 * -10 + x * -10) + x(-2 + x))
-48 + -34x + 5x2 = ((20 + -10x) + x(-2 + x))
-48 + -34x + 5x2 = (20 + -10x + (-2 * x + x * x))
-48 + -34x + 5x2 = (20 + -10x + (-2x + x2))

Combine like terms: -10x + -2x = -12x
-48 + -34x + 5x2 = (20 + -12x + x2)

Solving
-48 + -34x + 5x2 = 20 + -12x + x2

Solving for variable 'x'.

Reorder the terms:
-48 + -20 + -34x + 12x + 5x2 + -1x2 = 20 + -12x + x2 + -20 + 12x + -1x2

Combine like terms: -48 + -20 = -68
-68 + -34x + 12x + 5x2 + -1x2 = 20 + -12x + x2 + -20 + 12x + -1x2

Combine like terms: -34x + 12x = -22x
-68 + -22x + 5x2 + -1x2 = 20 + -12x + x2 + -20 + 12x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
-68 + -22x + 4x2 = 20 + -12x + x2 + -20 + 12x + -1x2

Reorder the terms:
-68 + -22x + 4x2 = 20 + -20 + -12x + 12x + x2 + -1x2

Combine like terms: 20 + -20 = 0
-68 + -22x + 4x2 = 0 + -12x + 12x + x2 + -1x2
-68 + -22x + 4x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
-68 + -22x + 4x2 = 0 + x2 + -1x2
-68 + -22x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-68 + -22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-34 + -11x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-34 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-34 + -11x + 2x2 = 0

Solving
-34 + -11x + 2x2 = 0

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

Divide each side by '2'.
-17 + -5.5x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -5.5x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -5.5x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -5.5x + x2 = 0 + 17
-5.5x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-5.5x + x2 = 17

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 17 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 17 + 7.5625

Combine like terms: 17 + 7.5625 = 24.5625
7.5625 + -5.5x + x2 = 24.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 24.5625

Calculate the square root of the right side: 4.9560569

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.9560569 and -4.9560569.

Subproblem 1
x + -2.75 = 4.9560569

Simplifying
x + -2.75 = 4.9560569

Reorder the terms:
-2.75 + x = 4.9560569

Solving
-2.75 + x = 4.9560569

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 4.9560569 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 4.9560569 + 2.75
x = 4.9560569 + 2.75

Combine like terms: 4.9560569 + 2.75 = 7.7060569
x = 7.7060569

Simplifying
x = 7.7060569

Subproblem 2
x + -2.75 = -4.9560569

Simplifying
x + -2.75 = -4.9560569

Reorder the terms:
-2.75 + x = -4.9560569

Solving
-2.75 + x = -4.9560569

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -4.9560569 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -4.9560569 + 2.75
x = -4.9560569 + 2.75

Combine like terms: -4.9560569 + 2.75 = -2.2060569
x = -2.2060569

Simplifying
x = -2.2060569

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.7060569, -2.2060569}
Solution
x = {7.7060569, -2.2060569}