3x^2=9(4x+4+9)

Solution for 3x^2=9(4x+4+9) equation:

Simplifying
3x2 = 9(4x + 4 + 9)

Reorder the terms:
3x2 = 9(4 + 9 + 4x)

Combine like terms: 4 + 9 = 13
3x2 = 9(13 + 4x)
3x2 = (13 * 9 + 4x * 9)
3x2 = (117 + 36x)

Solving
3x2 = 117 + 36x

Solving for variable 'x'.

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

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

Combine like terms: 117 + -117 = 0
-117 + -36x + 3x2 = 0 + 36x + -36x
-117 + -36x + 3x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
-117 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-39 + -12x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-39 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-39 + -12x + x2 = 0

Solving
-39 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -12x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + -12x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -12x + x2 = 0 + 39
-12x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
-12x + x2 = 39

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 39 + 36

Reorder the terms:
36 + -12x + x2 = 39 + 36

Combine like terms: 39 + 36 = 75
36 + -12x + x2 = 75

Factor a perfect square on the left side:
(x + -6)(x + -6) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -6) equal to 8.660254038 and -8.660254038.

Subproblem 1
x + -6 = 8.660254038

Simplifying
x + -6 = 8.660254038

Reorder the terms:
-6 + x = 8.660254038

Solving
-6 + x = 8.660254038

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 8.660254038 + 6

Combine like terms: -6 + 6 = 0
0 + x = 8.660254038 + 6
x = 8.660254038 + 6

Combine like terms: 8.660254038 + 6 = 14.660254038
x = 14.660254038

Simplifying
x = 14.660254038

Subproblem 2
x + -6 = -8.660254038

Simplifying
x + -6 = -8.660254038

Reorder the terms:
-6 + x = -8.660254038

Solving
-6 + x = -8.660254038

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -8.660254038 + 6

Combine like terms: -6 + 6 = 0
0 + x = -8.660254038 + 6
x = -8.660254038 + 6

Combine like terms: -8.660254038 + 6 = -2.660254038
x = -2.660254038

Simplifying
x = -2.660254038

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.660254038, -2.660254038}
Solution
x = {14.660254038, -2.660254038}