12x(x+6)=100

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Solution for 12x(x+6)=100 equation: 


Simplifying
12x(x + 6) = 100

Reorder the terms:
12x(6 + x) = 100
(6 * 12x + x * 12x) = 100
(72x + 12x2) = 100

Solving
72x + 12x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 72x + 12x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 72x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 18x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + 18x + 3x2)' equal to zero and attempt to solve:

Simplifying
-25 + 18x + 3x2 = 0

Solving
-25 + 18x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 6x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 6x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 6x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 6x + x2 = 0 + 8.333333333
6x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
6x + x2 = 8.333333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 8.333333333 + 9

Reorder the terms:
9 + 6x + x2 = 8.333333333 + 9

Combine like terms: 8.333333333 + 9 = 17.333333333
9 + 6x + x2 = 17.333333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 17.333333333

Calculate the square root of the right side: 4.163331999

Break this problem into two subproblems by setting 
(x + 3) equal to 4.163331999 and -4.163331999.


Subproblem 1
x + 3 = 4.163331999

Simplifying
x + 3 = 4.163331999

Reorder the terms:
3 + x = 4.163331999

Solving
3 + x = 4.163331999

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 4.163331999 + -3

Combine like terms: 3 + -3 = 0
0 + x = 4.163331999 + -3
x = 4.163331999 + -3

Combine like terms: 4.163331999 + -3 = 1.163331999
x = 1.163331999

Simplifying
x = 1.163331999


Subproblem 2
x + 3 = -4.163331999

Simplifying
x + 3 = -4.163331999

Reorder the terms:
3 + x = -4.163331999

Solving
3 + x = -4.163331999

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -4.163331999 + -3

Combine like terms: 3 + -3 = 0
0 + x = -4.163331999 + -3
x = -4.163331999 + -3

Combine like terms: -4.163331999 + -3 = -7.163331999
x = -7.163331999

Simplifying
x = -7.163331999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.163331999, -7.163331999}
Solution
x = {1.163331999, -7.163331999}

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