(15+2x)(18+2x)=360

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Solution for (15+2x)(18+2x)=360 equation: 


Simplifying
(15 + 2x)(18 + 2x) = 360

Multiply (15 + 2x) * (18 + 2x)
(15(18 + 2x) + 2x * (18 + 2x)) = 360
((18 * 15 + 2x * 15) + 2x * (18 + 2x)) = 360
((270 + 30x) + 2x * (18 + 2x)) = 360
(270 + 30x + (18 * 2x + 2x * 2x)) = 360
(270 + 30x + (36x + 4x2)) = 360

Combine like terms: 30x + 36x = 66x
(270 + 66x + 4x2) = 360

Solving
270 + 66x + 4x2 = 360

Solving for variable 'x'.

Reorder the terms:
270 + -360 + 66x + 4x2 = 360 + -360

Combine like terms: 270 + -360 = -90
-90 + 66x + 4x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-90 + 66x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 33x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 33x + 2x2)' equal to zero and attempt to solve:

Simplifying
-45 + 33x + 2x2 = 0

Solving
-45 + 33x + 2x2 = 0

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

Divide each side by '2'.
-22.5 + 16.5x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 16.5x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 16.5x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 16.5x + x2 = 0 + 22.5
16.5x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
16.5x + x2 = 22.5

The x term is 16.5x.  Take half its coefficient (8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
16.5x + 68.0625 + x2 = 22.5 + 68.0625

Reorder the terms:
68.0625 + 16.5x + x2 = 22.5 + 68.0625

Combine like terms: 22.5 + 68.0625 = 90.5625
68.0625 + 16.5x + x2 = 90.5625

Factor a perfect square on the left side:
(x + 8.25)(x + 8.25) = 90.5625

Calculate the square root of the right side: 9.516433155

Break this problem into two subproblems by setting 
(x + 8.25) equal to 9.516433155 and -9.516433155.


Subproblem 1
x + 8.25 = 9.516433155

Simplifying
x + 8.25 = 9.516433155

Reorder the terms:
8.25 + x = 9.516433155

Solving
8.25 + x = 9.516433155

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = 9.516433155 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = 9.516433155 + -8.25
x = 9.516433155 + -8.25

Combine like terms: 9.516433155 + -8.25 = 1.266433155
x = 1.266433155

Simplifying
x = 1.266433155


Subproblem 2
x + 8.25 = -9.516433155

Simplifying
x + 8.25 = -9.516433155

Reorder the terms:
8.25 + x = -9.516433155

Solving
8.25 + x = -9.516433155

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = -9.516433155 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = -9.516433155 + -8.25
x = -9.516433155 + -8.25

Combine like terms: -9.516433155 + -8.25 = -17.766433155
x = -17.766433155

Simplifying
x = -17.766433155


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.266433155, -17.766433155}
Solution
x = {1.266433155, -17.766433155}

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