(30-2x)(20-2x)=480

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Solution for (30-2x)(20-2x)=480 equation: 


Simplifying
(30 + -2x)(20 + -2x) = 480

Multiply (30 + -2x) * (20 + -2x)
(30(20 + -2x) + -2x * (20 + -2x)) = 480
((20 * 30 + -2x * 30) + -2x * (20 + -2x)) = 480
((600 + -60x) + -2x * (20 + -2x)) = 480
(600 + -60x + (20 * -2x + -2x * -2x)) = 480
(600 + -60x + (-40x + 4x2)) = 480

Combine like terms: -60x + -40x = -100x
(600 + -100x + 4x2) = 480

Solving
600 + -100x + 4x2 = 480

Solving for variable 'x'.

Reorder the terms:
600 + -480 + -100x + 4x2 = 480 + -480

Combine like terms: 600 + -480 = 120
120 + -100x + 4x2 = 480 + -480

Combine like terms: 480 + -480 = 0
120 + -100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -25x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(30 + -25x + x2)' equal to zero and attempt to solve:

Simplifying
30 + -25x + x2 = 0

Solving
30 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -25x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -25x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -25x + x2 = 0 + -30
-25x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-25x + x2 = -30

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -30 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -30 + 156.25

Combine like terms: -30 + 156.25 = 126.25
156.25 + -25x + x2 = 126.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 126.25

Calculate the square root of the right side: 11.236102527

Break this problem into two subproblems by setting 
(x + -12.5) equal to 11.236102527 and -11.236102527.


Subproblem 1
x + -12.5 = 11.236102527

Simplifying
x + -12.5 = 11.236102527

Reorder the terms:
-12.5 + x = 11.236102527

Solving
-12.5 + x = 11.236102527

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 11.236102527 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 11.236102527 + 12.5
x = 11.236102527 + 12.5

Combine like terms: 11.236102527 + 12.5 = 23.736102527
x = 23.736102527

Simplifying
x = 23.736102527


Subproblem 2
x + -12.5 = -11.236102527

Simplifying
x + -12.5 = -11.236102527

Reorder the terms:
-12.5 + x = -11.236102527

Solving
-12.5 + x = -11.236102527

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -11.236102527 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -11.236102527 + 12.5
x = -11.236102527 + 12.5

Combine like terms: -11.236102527 + 12.5 = 1.263897473
x = 1.263897473

Simplifying
x = 1.263897473


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.736102527, 1.263897473}
Solution
x = {23.736102527, 1.263897473}

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