(14-2x)*(11-2x)=80

Solution for (14-2x)*(11-2x)=80 equation:

Simplifying
(14 + -2x)(11 + -2x) = 80

Multiply (14 + -2x) * (11 + -2x)
(14(11 + -2x) + -2x * (11 + -2x)) = 80
((11 * 14 + -2x * 14) + -2x * (11 + -2x)) = 80
((154 + -28x) + -2x * (11 + -2x)) = 80
(154 + -28x + (11 * -2x + -2x * -2x)) = 80
(154 + -28x + (-22x + 4x2)) = 80

Combine like terms: -28x + -22x = -50x
(154 + -50x + 4x2) = 80

Solving
154 + -50x + 4x2 = 80

Solving for variable 'x'.

Reorder the terms:
154 + -80 + -50x + 4x2 = 80 + -80

Combine like terms: 154 + -80 = 74
74 + -50x + 4x2 = 80 + -80

Combine like terms: 80 + -80 = 0
74 + -50x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(37 + -25x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(37 + -25x + 2x2)' equal to zero and attempt to solve:

Simplifying
37 + -25x + 2x2 = 0

Solving
37 + -25x + 2x2 = 0

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

Divide each side by '2'.
18.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-18.5' to each side of the equation.
18.5 + -12.5x + -18.5 + x2 = 0 + -18.5

Reorder the terms:
18.5 + -18.5 + -12.5x + x2 = 0 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + -12.5x + x2 = 0 + -18.5
-12.5x + x2 = 0 + -18.5

Combine like terms: 0 + -18.5 = -18.5
-12.5x + x2 = -18.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -18.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -18.5 + 39.0625

Combine like terms: -18.5 + 39.0625 = 20.5625
39.0625 + -12.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + -6.25) equal to 4.534589287 and -4.534589287.

Subproblem 1
x + -6.25 = 4.534589287

Simplifying
x + -6.25 = 4.534589287

Reorder the terms:
-6.25 + x = 4.534589287

Solving
-6.25 + x = 4.534589287

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 4.534589287 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 4.534589287 + 6.25
x = 4.534589287 + 6.25

Combine like terms: 4.534589287 + 6.25 = 10.784589287
x = 10.784589287

Simplifying
x = 10.784589287

Subproblem 2
x + -6.25 = -4.534589287

Simplifying
x + -6.25 = -4.534589287

Reorder the terms:
-6.25 + x = -4.534589287

Solving
-6.25 + x = -4.534589287

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -4.534589287 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -4.534589287 + 6.25
x = -4.534589287 + 6.25

Combine like terms: -4.534589287 + 6.25 = 1.715410713
x = 1.715410713

Simplifying
x = 1.715410713

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.784589287, 1.715410713}
Solution
x = {10.784589287, 1.715410713}