(18+2X)(12+2X)=324

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Solution for (18+2X)(12+2X)=324 equation: 


Simplifying
(18 + 2X)(12 + 2X) = 324

Multiply (18 + 2X) * (12 + 2X)
(18(12 + 2X) + 2X * (12 + 2X)) = 324
((12 * 18 + 2X * 18) + 2X * (12 + 2X)) = 324
((216 + 36X) + 2X * (12 + 2X)) = 324
(216 + 36X + (12 * 2X + 2X * 2X)) = 324
(216 + 36X + (24X + 4X2)) = 324

Combine like terms: 36X + 24X = 60X
(216 + 60X + 4X2) = 324

Solving
216 + 60X + 4X2 = 324

Solving for variable 'X'.

Reorder the terms:
216 + -324 + 60X + 4X2 = 324 + -324

Combine like terms: 216 + -324 = -108
-108 + 60X + 4X2 = 324 + -324

Combine like terms: 324 + -324 = 0
-108 + 60X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + 15X + X2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-27 + 15X + X2)' equal to zero and attempt to solve:

Simplifying
-27 + 15X + X2 = 0

Solving
-27 + 15X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 15X + 27 + X2 = 0 + 27

Reorder the terms:
-27 + 27 + 15X + X2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 15X + X2 = 0 + 27
15X + X2 = 0 + 27

Combine like terms: 0 + 27 = 27
15X + X2 = 27

The X term is 15X.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15X + 56.25 + X2 = 27 + 56.25

Reorder the terms:
56.25 + 15X + X2 = 27 + 56.25

Combine like terms: 27 + 56.25 = 83.25
56.25 + 15X + X2 = 83.25

Factor a perfect square on the left side:
(X + 7.5)(X + 7.5) = 83.25

Calculate the square root of the right side: 9.124143795

Break this problem into two subproblems by setting 
(X + 7.5) equal to 9.124143795 and -9.124143795.


Subproblem 1
X + 7.5 = 9.124143795

Simplifying
X + 7.5 = 9.124143795

Reorder the terms:
7.5 + X = 9.124143795

Solving
7.5 + X = 9.124143795

Solving for variable 'X'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + X = 9.124143795 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + X = 9.124143795 + -7.5
X = 9.124143795 + -7.5

Combine like terms: 9.124143795 + -7.5 = 1.624143795
X = 1.624143795

Simplifying
X = 1.624143795


Subproblem 2
X + 7.5 = -9.124143795

Simplifying
X + 7.5 = -9.124143795

Reorder the terms:
7.5 + X = -9.124143795

Solving
7.5 + X = -9.124143795

Solving for variable 'X'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + X = -9.124143795 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + X = -9.124143795 + -7.5
X = -9.124143795 + -7.5

Combine like terms: -9.124143795 + -7.5 = -16.624143795
X = -16.624143795

Simplifying
X = -16.624143795


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.624143795, -16.624143795}
Solution
X = {1.624143795, -16.624143795}

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