360=720-(30+2x)(24+2x)

Solution for 360=720-(30+2x)(24+2x) equation:

Simplifying
360 = 720 + -1(30 + 2x)(24 + 2x)

Multiply (30 + 2x) * (24 + 2x)
360 = 720 + -1(30(24 + 2x) + 2x * (24 + 2x))
360 = 720 + -1((24 * 30 + 2x * 30) + 2x * (24 + 2x))
360 = 720 + -1((720 + 60x) + 2x * (24 + 2x))
360 = 720 + -1(720 + 60x + (24 * 2x + 2x * 2x))
360 = 720 + -1(720 + 60x + (48x + 4x2))

Combine like terms: 60x + 48x = 108x
360 = 720 + -1(720 + 108x + 4x2)
360 = 720 + (720 * -1 + 108x * -1 + 4x2 * -1)
360 = 720 + (-720 + -108x + -4x2)

Combine like terms: 720 + -720 = 0
360 = 0 + -108x + -4x2
360 = -108x + -4x2

Solving
360 = -108x + -4x2

Solving for variable 'x'.

Reorder the terms:
360 + 108x + 4x2 = -108x + 108x + -4x2 + 4x2

Combine like terms: -108x + 108x = 0
360 + 108x + 4x2 = 0 + -4x2 + 4x2
360 + 108x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
360 + 108x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(90 + 27x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(90 + 27x + x2)' equal to zero and attempt to solve:

Simplifying
90 + 27x + x2 = 0

Solving
90 + 27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + 27x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + 27x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + 27x + x2 = 0 + -90
27x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
27x + x2 = -90

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = -90 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -90 + 182.25

Combine like terms: -90 + 182.25 = 92.25
182.25 + 27x + x2 = 92.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + 13.5) equal to 9.604686356 and -9.604686356.

Subproblem 1
x + 13.5 = 9.604686356

Simplifying
x + 13.5 = 9.604686356

Reorder the terms:
13.5 + x = 9.604686356

Solving
13.5 + x = 9.604686356

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 9.604686356 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 9.604686356 + -13.5
x = 9.604686356 + -13.5

Combine like terms: 9.604686356 + -13.5 = -3.895313644
x = -3.895313644

Simplifying
x = -3.895313644

Subproblem 2
x + 13.5 = -9.604686356

Simplifying
x + 13.5 = -9.604686356

Reorder the terms:
13.5 + x = -9.604686356

Solving
13.5 + x = -9.604686356

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -9.604686356 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -9.604686356 + -13.5
x = -9.604686356 + -13.5

Combine like terms: -9.604686356 + -13.5 = -23.104686356
x = -23.104686356

Simplifying
x = -23.104686356

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.895313644, -23.104686356}
Solution
x = {-3.895313644, -23.104686356}