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 = 5
3x2 = 9(5 + 4x)
3x2 = (5 * 9 + 4x * 9)
3x2 = (45 + 36x)

Solving
3x2 = 45 + 36x

Solving for variable 'x'.

Reorder the terms:
-45 + -36x + 3x2 = 45 + 36x + -45 + -36x

Reorder the terms:
-45 + -36x + 3x2 = 45 + -45 + 36x + -36x

Combine like terms: 45 + -45 = 0
-45 + -36x + 3x2 = 0 + 36x + -36x
-45 + -36x + 3x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
-45 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -12x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-15 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + -12x + x2 = 0

Solving
-15 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -12x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -12x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -12x + x2 = 0 + 15
-12x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-12x + x2 = 15

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 = 15 + 36

Reorder the terms:
36 + -12x + x2 = 15 + 36

Combine like terms: 15 + 36 = 51
36 + -12x + x2 = 51

Factor a perfect square on the left side:
(x + -6)(x + -6) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -6) equal to 7.141428429 and -7.141428429.

Subproblem 1
x + -6 = 7.141428429

Simplifying
x + -6 = 7.141428429

Reorder the terms:
-6 + x = 7.141428429

Solving
-6 + x = 7.141428429

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 = 7.141428429 + 6

Combine like terms: -6 + 6 = 0
0 + x = 7.141428429 + 6
x = 7.141428429 + 6

Combine like terms: 7.141428429 + 6 = 13.141428429
x = 13.141428429

Simplifying
x = 13.141428429

Subproblem 2
x + -6 = -7.141428429

Simplifying
x + -6 = -7.141428429

Reorder the terms:
-6 + x = -7.141428429

Solving
-6 + x = -7.141428429

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 = -7.141428429 + 6

Combine like terms: -6 + 6 = 0
0 + x = -7.141428429 + 6
x = -7.141428429 + 6

Combine like terms: -7.141428429 + 6 = -1.141428429
x = -1.141428429

Simplifying
x = -1.141428429

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.141428429, -1.141428429}
Solution
x = {13.141428429, -1.141428429}