(60-2x)(40-2x)=832

Solution for (60-2x)(40-2x)=832 equation:

Simplifying
(60 + -2x)(40 + -2x) = 832

Multiply (60 + -2x) * (40 + -2x)
(60(40 + -2x) + -2x * (40 + -2x)) = 832
((40 * 60 + -2x * 60) + -2x * (40 + -2x)) = 832
((2400 + -120x) + -2x * (40 + -2x)) = 832
(2400 + -120x + (40 * -2x + -2x * -2x)) = 832
(2400 + -120x + (-80x + 4x2)) = 832

Combine like terms: -120x + -80x = -200x
(2400 + -200x + 4x2) = 832

Solving
2400 + -200x + 4x2 = 832

Solving for variable 'x'.

Reorder the terms:
2400 + -832 + -200x + 4x2 = 832 + -832

Combine like terms: 2400 + -832 = 1568
1568 + -200x + 4x2 = 832 + -832

Combine like terms: 832 + -832 = 0
1568 + -200x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(392 + -50x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(392 + -50x + x2)' equal to zero and attempt to solve:

Simplifying
392 + -50x + x2 = 0

Solving
392 + -50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-392' to each side of the equation.
392 + -50x + -392 + x2 = 0 + -392

Reorder the terms:
392 + -392 + -50x + x2 = 0 + -392

Combine like terms: 392 + -392 = 0
0 + -50x + x2 = 0 + -392
-50x + x2 = 0 + -392

Combine like terms: 0 + -392 = -392
-50x + x2 = -392

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -392 + 625

Reorder the terms:
625 + -50x + x2 = -392 + 625

Combine like terms: -392 + 625 = 233
625 + -50x + x2 = 233

Factor a perfect square on the left side:
(x + -25)(x + -25) = 233

Calculate the square root of the right side: 15.264337522

Break this problem into two subproblems by setting 
(x + -25) equal to 15.264337522 and -15.264337522.

Subproblem 1
x + -25 = 15.264337522

Simplifying
x + -25 = 15.264337522

Reorder the terms:
-25 + x = 15.264337522

Solving
-25 + x = 15.264337522

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = 15.264337522 + 25

Combine like terms: -25 + 25 = 0
0 + x = 15.264337522 + 25
x = 15.264337522 + 25

Combine like terms: 15.264337522 + 25 = 40.264337522
x = 40.264337522

Simplifying
x = 40.264337522

Subproblem 2
x + -25 = -15.264337522

Simplifying
x + -25 = -15.264337522

Reorder the terms:
-25 + x = -15.264337522

Solving
-25 + x = -15.264337522

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = -15.264337522 + 25

Combine like terms: -25 + 25 = 0
0 + x = -15.264337522 + 25
x = -15.264337522 + 25

Combine like terms: -15.264337522 + 25 = 9.735662478
x = 9.735662478

Simplifying
x = 9.735662478

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40.264337522, 9.735662478}
Solution
x = {40.264337522, 9.735662478}