(x)(x+15)(9)=1218

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Solution for (x)(x+15)(9)=1218 equation: 


Simplifying
(x)(x + 15)(9) = 1218

Reorder the terms:
x(15 + x)(9) = 1218

Reorder the terms for easier multiplication:
9x(15 + x) = 1218
(15 * 9x + x * 9x) = 1218
(135x + 9x2) = 1218

Solving
135x + 9x2 = 1218

Solving for variable 'x'.

Reorder the terms:
-1218 + 135x + 9x2 = 1218 + -1218

Combine like terms: 1218 + -1218 = 0
-1218 + 135x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-406 + 45x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-406 + 45x + 3x2)' equal to zero and attempt to solve:

Simplifying
-406 + 45x + 3x2 = 0

Solving
-406 + 45x + 3x2 = 0

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

Divide each side by '3'.
-135.3333333 + 15x + x2 = 0

Move the constant term to the right:

Add '135.3333333' to each side of the equation.
-135.3333333 + 15x + 135.3333333 + x2 = 0 + 135.3333333

Reorder the terms:
-135.3333333 + 135.3333333 + 15x + x2 = 0 + 135.3333333

Combine like terms: -135.3333333 + 135.3333333 = 0.0000000
0.0000000 + 15x + x2 = 0 + 135.3333333
15x + x2 = 0 + 135.3333333

Combine like terms: 0 + 135.3333333 = 135.3333333
15x + x2 = 135.3333333

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 = 135.3333333 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 135.3333333 + 56.25

Combine like terms: 135.3333333 + 56.25 = 191.5833333
56.25 + 15x + x2 = 191.5833333

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 191.5833333

Calculate the square root of the right side: 13.84136313

Break this problem into two subproblems by setting 
(x + 7.5) equal to 13.84136313 and -13.84136313.


Subproblem 1
x + 7.5 = 13.84136313

Simplifying
x + 7.5 = 13.84136313

Reorder the terms:
7.5 + x = 13.84136313

Solving
7.5 + x = 13.84136313

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 = 13.84136313 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 13.84136313 + -7.5
x = 13.84136313 + -7.5

Combine like terms: 13.84136313 + -7.5 = 6.34136313
x = 6.34136313

Simplifying
x = 6.34136313


Subproblem 2
x + 7.5 = -13.84136313

Simplifying
x + 7.5 = -13.84136313

Reorder the terms:
7.5 + x = -13.84136313

Solving
7.5 + x = -13.84136313

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 = -13.84136313 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -13.84136313 + -7.5
x = -13.84136313 + -7.5

Combine like terms: -13.84136313 + -7.5 = -21.34136313
x = -21.34136313

Simplifying
x = -21.34136313


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.34136313, -21.34136313}
Solution
x = {6.34136313, -21.34136313}

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