324=5(x(9+x)+x(9+x)+(12+2x)+(12+2x))

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Solution for 324=5(x(9+x)+x(9+x)+(12+2x)+(12+2x)) equation: 


Simplifying
324 = 5(x(9 + x) + x(9 + x) + (12 + 2x) + (12 + 2x))
324 = 5((9 * x + x * x) + x(9 + x) + (12 + 2x) + (12 + 2x))
324 = 5((9x + x2) + x(9 + x) + (12 + 2x) + (12 + 2x))
324 = 5(9x + x2 + (9 * x + x * x) + (12 + 2x) + (12 + 2x))
324 = 5(9x + x2 + (9x + x2) + (12 + 2x) + (12 + 2x))

Remove parenthesis around (12 + 2x)
324 = 5(9x + x2 + 9x + x2 + 12 + 2x + (12 + 2x))

Remove parenthesis around (12 + 2x)
324 = 5(9x + x2 + 9x + x2 + 12 + 2x + 12 + 2x)

Reorder the terms:
324 = 5(12 + 12 + 9x + 9x + 2x + 2x + x2 + x2)

Combine like terms: 12 + 12 = 24
324 = 5(24 + 9x + 9x + 2x + 2x + x2 + x2)

Combine like terms: 9x + 9x = 18x
324 = 5(24 + 18x + 2x + 2x + x2 + x2)

Combine like terms: 18x + 2x = 20x
324 = 5(24 + 20x + 2x + x2 + x2)

Combine like terms: 20x + 2x = 22x
324 = 5(24 + 22x + x2 + x2)

Combine like terms: x2 + x2 = 2x2
324 = 5(24 + 22x + 2x2)
324 = (24 * 5 + 22x * 5 + 2x2 * 5)
324 = (120 + 110x + 10x2)

Solving
324 = 120 + 110x + 10x2

Solving for variable 'x'.

Combine like terms: 324 + -120 = 204
204 + -110x + -10x2 = 120 + 110x + 10x2 + -120 + -110x + -10x2

Reorder the terms:
204 + -110x + -10x2 = 120 + -120 + 110x + -110x + 10x2 + -10x2

Combine like terms: 120 + -120 = 0
204 + -110x + -10x2 = 0 + 110x + -110x + 10x2 + -10x2
204 + -110x + -10x2 = 110x + -110x + 10x2 + -10x2

Combine like terms: 110x + -110x = 0
204 + -110x + -10x2 = 0 + 10x2 + -10x2
204 + -110x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
204 + -110x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(102 + -55x + -5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(102 + -55x + -5x2)' equal to zero and attempt to solve:

Simplifying
102 + -55x + -5x2 = 0

Solving
102 + -55x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-20.4 + 11x + x2 = 0

Move the constant term to the right:

Add '20.4' to each side of the equation.
-20.4 + 11x + 20.4 + x2 = 0 + 20.4

Reorder the terms:
-20.4 + 20.4 + 11x + x2 = 0 + 20.4

Combine like terms: -20.4 + 20.4 = 0.0
0.0 + 11x + x2 = 0 + 20.4
11x + x2 = 0 + 20.4

Combine like terms: 0 + 20.4 = 20.4
11x + x2 = 20.4

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 20.4 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 20.4 + 30.25

Combine like terms: 20.4 + 30.25 = 50.65
30.25 + 11x + x2 = 50.65

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 50.65

Calculate the square root of the right side: 7.116881339

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7.116881339 and -7.116881339.


Subproblem 1
x + 5.5 = 7.116881339

Simplifying
x + 5.5 = 7.116881339

Reorder the terms:
5.5 + x = 7.116881339

Solving
5.5 + x = 7.116881339

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 7.116881339 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 7.116881339 + -5.5
x = 7.116881339 + -5.5

Combine like terms: 7.116881339 + -5.5 = 1.616881339
x = 1.616881339

Simplifying
x = 1.616881339


Subproblem 2
x + 5.5 = -7.116881339

Simplifying
x + 5.5 = -7.116881339

Reorder the terms:
5.5 + x = -7.116881339

Solving
5.5 + x = -7.116881339

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -7.116881339 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -7.116881339 + -5.5
x = -7.116881339 + -5.5

Combine like terms: -7.116881339 + -5.5 = -12.616881339
x = -12.616881339

Simplifying
x = -12.616881339


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.616881339, -12.616881339}
Solution
x = {1.616881339, -12.616881339}

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