784=(20-2x)(40-2x)

Solution for 784=(20-2x)(40-2x) equation:

Simplifying
784 = (20 + -2x)(40 + -2x)

Multiply (20 + -2x) * (40 + -2x)
784 = (20(40 + -2x) + -2x * (40 + -2x))
784 = ((40 * 20 + -2x * 20) + -2x * (40 + -2x))
784 = ((800 + -40x) + -2x * (40 + -2x))
784 = (800 + -40x + (40 * -2x + -2x * -2x))
784 = (800 + -40x + (-80x + 4x2))

Combine like terms: -40x + -80x = -120x
784 = (800 + -120x + 4x2)

Solving
784 = 800 + -120x + 4x2

Solving for variable 'x'.

Combine like terms: 784 + -800 = -16
-16 + 120x + -4x2 = 800 + -120x + 4x2 + -800 + 120x + -4x2

Reorder the terms:
-16 + 120x + -4x2 = 800 + -800 + -120x + 120x + 4x2 + -4x2

Combine like terms: 800 + -800 = 0
-16 + 120x + -4x2 = 0 + -120x + 120x + 4x2 + -4x2
-16 + 120x + -4x2 = -120x + 120x + 4x2 + -4x2

Combine like terms: -120x + 120x = 0
-16 + 120x + -4x2 = 0 + 4x2 + -4x2
-16 + 120x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-16 + 120x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 30x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + 30x + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + 30x + -1x2 = 0

Solving
-4 + 30x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -30x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -30x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -30x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -30x + x2 = 0 + -4
-30x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-30x + x2 = -4

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -4 + 225

Reorder the terms:
225 + -30x + x2 = -4 + 225

Combine like terms: -4 + 225 = 221
225 + -30x + x2 = 221

Factor a perfect square on the left side:
(x + -15)(x + -15) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(x + -15) equal to 14.866068747 and -14.866068747.

Subproblem 1
x + -15 = 14.866068747

Simplifying
x + -15 = 14.866068747

Reorder the terms:
-15 + x = 14.866068747

Solving
-15 + x = 14.866068747

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 14.866068747 + 15

Combine like terms: -15 + 15 = 0
0 + x = 14.866068747 + 15
x = 14.866068747 + 15

Combine like terms: 14.866068747 + 15 = 29.866068747
x = 29.866068747

Simplifying
x = 29.866068747

Subproblem 2
x + -15 = -14.866068747

Simplifying
x + -15 = -14.866068747

Reorder the terms:
-15 + x = -14.866068747

Solving
-15 + x = -14.866068747

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -14.866068747 + 15

Combine like terms: -15 + 15 = 0
0 + x = -14.866068747 + 15
x = -14.866068747 + 15

Combine like terms: -14.866068747 + 15 = 0.133931253
x = 0.133931253

Simplifying
x = 0.133931253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.866068747, 0.133931253}
Solution
x = {29.866068747, 0.133931253}