(x-1)(2x-8)=132

Solution for (x-1)(2x-8)=132 equation:

Simplifying
(x + -1)(2x + -8) = 132

Reorder the terms:
(-1 + x)(2x + -8) = 132

Reorder the terms:
(-1 + x)(-8 + 2x) = 132

Multiply (-1 + x) * (-8 + 2x)
(-1(-8 + 2x) + x(-8 + 2x)) = 132
((-8 * -1 + 2x * -1) + x(-8 + 2x)) = 132
((8 + -2x) + x(-8 + 2x)) = 132
(8 + -2x + (-8 * x + 2x * x)) = 132
(8 + -2x + (-8x + 2x2)) = 132

Combine like terms: -2x + -8x = -10x
(8 + -10x + 2x2) = 132

Solving
8 + -10x + 2x2 = 132

Solving for variable 'x'.

Reorder the terms:
8 + -132 + -10x + 2x2 = 132 + -132

Combine like terms: 8 + -132 = -124
-124 + -10x + 2x2 = 132 + -132

Combine like terms: 132 + -132 = 0
-124 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-62 + -5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-62 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-62 + -5x + x2 = 0

Solving
-62 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -5x + 62 + x2 = 0 + 62

Reorder the terms:
-62 + 62 + -5x + x2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -5x + x2 = 0 + 62
-5x + x2 = 0 + 62

Combine like terms: 0 + 62 = 62
-5x + x2 = 62

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 62 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 62 + 6.25

Combine like terms: 62 + 6.25 = 68.25
6.25 + -5x + x2 = 68.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x + -2.5) equal to 8.261355821 and -8.261355821.

Subproblem 1
x + -2.5 = 8.261355821

Simplifying
x + -2.5 = 8.261355821

Reorder the terms:
-2.5 + x = 8.261355821

Solving
-2.5 + x = 8.261355821

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 8.261355821 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 8.261355821 + 2.5
x = 8.261355821 + 2.5

Combine like terms: 8.261355821 + 2.5 = 10.761355821
x = 10.761355821

Simplifying
x = 10.761355821

Subproblem 2
x + -2.5 = -8.261355821

Simplifying
x + -2.5 = -8.261355821

Reorder the terms:
-2.5 + x = -8.261355821

Solving
-2.5 + x = -8.261355821

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -8.261355821 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -8.261355821 + 2.5
x = -8.261355821 + 2.5

Combine like terms: -8.261355821 + 2.5 = -5.761355821
x = -5.761355821

Simplifying
x = -5.761355821

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.761355821, -5.761355821}
Solution
x = {10.761355821, -5.761355821}