(8-2x)(16-2x)=82

Solution for (8-2x)(16-2x)=82 equation:

Simplifying
(8 + -2x)(16 + -2x) = 82

Multiply (8 + -2x) * (16 + -2x)
(8(16 + -2x) + -2x * (16 + -2x)) = 82
((16 * 8 + -2x * 8) + -2x * (16 + -2x)) = 82
((128 + -16x) + -2x * (16 + -2x)) = 82
(128 + -16x + (16 * -2x + -2x * -2x)) = 82
(128 + -16x + (-32x + 4x2)) = 82

Combine like terms: -16x + -32x = -48x
(128 + -48x + 4x2) = 82

Solving
128 + -48x + 4x2 = 82

Solving for variable 'x'.

Reorder the terms:
128 + -82 + -48x + 4x2 = 82 + -82

Combine like terms: 128 + -82 = 46
46 + -48x + 4x2 = 82 + -82

Combine like terms: 82 + -82 = 0
46 + -48x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + -24x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(23 + -24x + 2x2)' equal to zero and attempt to solve:

Simplifying
23 + -24x + 2x2 = 0

Solving
23 + -24x + 2x2 = 0

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

Divide each side by '2'.
11.5 + -12x + x2 = 0

Move the constant term to the right:

Add '-11.5' to each side of the equation.
11.5 + -12x + -11.5 + x2 = 0 + -11.5

Reorder the terms:
11.5 + -11.5 + -12x + x2 = 0 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + -12x + x2 = 0 + -11.5
-12x + x2 = 0 + -11.5

Combine like terms: 0 + -11.5 = -11.5
-12x + x2 = -11.5

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -11.5 + 36

Reorder the terms:
36 + -12x + x2 = -11.5 + 36

Combine like terms: -11.5 + 36 = 24.5
36 + -12x + x2 = 24.5

Factor a perfect square on the left side:
(x + -6)(x + -6) = 24.5

Calculate the square root of the right side: 4.949747468

Break this problem into two subproblems by setting 
(x + -6) equal to 4.949747468 and -4.949747468.

Subproblem 1
x + -6 = 4.949747468

Simplifying
x + -6 = 4.949747468

Reorder the terms:
-6 + x = 4.949747468

Solving
-6 + x = 4.949747468

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 4.949747468 + 6

Combine like terms: -6 + 6 = 0
0 + x = 4.949747468 + 6
x = 4.949747468 + 6

Combine like terms: 4.949747468 + 6 = 10.949747468
x = 10.949747468

Simplifying
x = 10.949747468

Subproblem 2
x + -6 = -4.949747468

Simplifying
x + -6 = -4.949747468

Reorder the terms:
-6 + x = -4.949747468

Solving
-6 + x = -4.949747468

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -4.949747468 + 6

Combine like terms: -6 + 6 = 0
0 + x = -4.949747468 + 6
x = -4.949747468 + 6

Combine like terms: -4.949747468 + 6 = 1.050252532
x = 1.050252532

Simplifying
x = 1.050252532

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.949747468, 1.050252532}
Solution
x = {10.949747468, 1.050252532}