12x(x+3)-3x=117

Solution for 12x(x+3)-3x=117 equation:

Simplifying
12x(x + 3) + -3x = 117

Reorder the terms:
12x(3 + x) + -3x = 117
(3 * 12x + x * 12x) + -3x = 117
(36x + 12x2) + -3x = 117

Reorder the terms:
36x + -3x + 12x2 = 117

Combine like terms: 36x + -3x = 33x
33x + 12x2 = 117

Solving
33x + 12x2 = 117

Solving for variable 'x'.

Reorder the terms:
-117 + 33x + 12x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-117 + 33x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-39 + 11x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-39 + 11x + 4x2)' equal to zero and attempt to solve:

Simplifying
-39 + 11x + 4x2 = 0

Solving
-39 + 11x + 4x2 = 0

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

Divide each side by '4'.
-9.75 + 2.75x + x2 = 0

Move the constant term to the right:

Add '9.75' to each side of the equation.
-9.75 + 2.75x + 9.75 + x2 = 0 + 9.75

Reorder the terms:
-9.75 + 9.75 + 2.75x + x2 = 0 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + 2.75x + x2 = 0 + 9.75
2.75x + x2 = 0 + 9.75

Combine like terms: 0 + 9.75 = 9.75
2.75x + x2 = 9.75

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = 9.75 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = 9.75 + 1.890625

Combine like terms: 9.75 + 1.890625 = 11.640625
1.890625 + 2.75x + x2 = 11.640625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 11.640625

Calculate the square root of the right side: 3.411836016

Break this problem into two subproblems by setting 
(x + 1.375) equal to 3.411836016 and -3.411836016.

Subproblem 1
x + 1.375 = 3.411836016

Simplifying
x + 1.375 = 3.411836016

Reorder the terms:
1.375 + x = 3.411836016

Solving
1.375 + x = 3.411836016

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = 3.411836016 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = 3.411836016 + -1.375
x = 3.411836016 + -1.375

Combine like terms: 3.411836016 + -1.375 = 2.036836016
x = 2.036836016

Simplifying
x = 2.036836016

Subproblem 2
x + 1.375 = -3.411836016

Simplifying
x + 1.375 = -3.411836016

Reorder the terms:
1.375 + x = -3.411836016

Solving
1.375 + x = -3.411836016

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = -3.411836016 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = -3.411836016 + -1.375
x = -3.411836016 + -1.375

Combine like terms: -3.411836016 + -1.375 = -4.786836016
x = -4.786836016

Simplifying
x = -4.786836016

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.036836016, -4.786836016}
Solution
x = {2.036836016, -4.786836016}