(9x)(3x+12)=180

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Solution for (9x)(3x+12)=180 equation:


Simplifying
(9x)(3x + 12) = 180

Remove parenthesis around (9x)
9x(3x + 12) = 180

Reorder the terms:
9x(12 + 3x) = 180
(12 * 9x + 3x * 9x) = 180
(108x + 27x2) = 180

Solving
108x + 27x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 108x + 27x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 108x + 27x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-20 + 12x + 3x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-20 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-20 + 12x + 3x2 = 0

Solving
-20 + 12x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + 4x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 4x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 4x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 4x + x2 = 0 + 6.666666667
4x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
4x + x2 = 6.666666667

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 6.666666667 + 4

Reorder the terms:
4 + 4x + x2 = 6.666666667 + 4

Combine like terms: 6.666666667 + 4 = 10.666666667
4 + 4x + x2 = 10.666666667

Factor a perfect square on the left side:
(x + 2)(x + 2) = 10.666666667

Calculate the square root of the right side: 3.265986324

Break this problem into two subproblems by setting 
(x + 2) equal to 3.265986324 and -3.265986324.


Subproblem 1
x + 2 = 3.265986324

Simplifying
x + 2 = 3.265986324

Reorder the terms:
2 + x = 3.265986324

Solving
2 + x = 3.265986324

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.265986324 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.265986324 + -2
x = 3.265986324 + -2

Combine like terms: 3.265986324 + -2 = 1.265986324
x = 1.265986324

Simplifying
x = 1.265986324


Subproblem 2
x + 2 = -3.265986324

Simplifying
x + 2 = -3.265986324

Reorder the terms:
2 + x = -3.265986324

Solving
2 + x = -3.265986324

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.265986324 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.265986324 + -2
x = -3.265986324 + -2

Combine like terms: -3.265986324 + -2 = -5.265986324
x = -5.265986324

Simplifying
x = -5.265986324


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.265986324, -5.265986324}
Solution
x = {1.265986324, -5.265986324}

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