(20-2x)(14-2x)=84

Solution for (20-2x)(14-2x)=84 equation:

Simplifying
(20 + -2x)(14 + -2x) = 84

Multiply (20 + -2x) * (14 + -2x)
(20(14 + -2x) + -2x * (14 + -2x)) = 84
((14 * 20 + -2x * 20) + -2x * (14 + -2x)) = 84
((280 + -40x) + -2x * (14 + -2x)) = 84
(280 + -40x + (14 * -2x + -2x * -2x)) = 84
(280 + -40x + (-28x + 4x2)) = 84

Combine like terms: -40x + -28x = -68x
(280 + -68x + 4x2) = 84

Solving
280 + -68x + 4x2 = 84

Solving for variable 'x'.

Reorder the terms:
280 + -84 + -68x + 4x2 = 84 + -84

Combine like terms: 280 + -84 = 196
196 + -68x + 4x2 = 84 + -84

Combine like terms: 84 + -84 = 0
196 + -68x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(49 + -17x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(49 + -17x + x2)' equal to zero and attempt to solve:

Simplifying
49 + -17x + x2 = 0

Solving
49 + -17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -17x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + -17x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -17x + x2 = 0 + -49
-17x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
-17x + x2 = -49

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -49 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -49 + 72.25

Combine like terms: -49 + 72.25 = 23.25
72.25 + -17x + x2 = 23.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + -8.5) equal to 4.82182538 and -4.82182538.

Subproblem 1
x + -8.5 = 4.82182538

Simplifying
x + -8.5 = 4.82182538

Reorder the terms:
-8.5 + x = 4.82182538

Solving
-8.5 + x = 4.82182538

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 4.82182538 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 4.82182538 + 8.5
x = 4.82182538 + 8.5

Combine like terms: 4.82182538 + 8.5 = 13.32182538
x = 13.32182538

Simplifying
x = 13.32182538

Subproblem 2
x + -8.5 = -4.82182538

Simplifying
x + -8.5 = -4.82182538

Reorder the terms:
-8.5 + x = -4.82182538

Solving
-8.5 + x = -4.82182538

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -4.82182538 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -4.82182538 + 8.5
x = -4.82182538 + 8.5

Combine like terms: -4.82182538 + 8.5 = 3.67817462
x = 3.67817462

Simplifying
x = 3.67817462

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.32182538, 3.67817462}
Solution
x = {13.32182538, 3.67817462}