0=-0.333(x+3)(x+3)+9

Solution for 0=-0.333(x+3)(x+3)+9 equation:

Simplifying
0 = -0.333(x + 3)(x + 3) + 9

Reorder the terms:
0 = -0.333(3 + x)(x + 3) + 9

Reorder the terms:
0 = -0.333(3 + x)(3 + x) + 9

Multiply (3 + x) * (3 + x)
0 = -0.333(3(3 + x) + x(3 + x)) + 9
0 = -0.333((3 * 3 + x * 3) + x(3 + x)) + 9
0 = -0.333((9 + 3x) + x(3 + x)) + 9
0 = -0.333(9 + 3x + (3 * x + x * x)) + 9
0 = -0.333(9 + 3x + (3x + x2)) + 9

Combine like terms: 3x + 3x = 6x
0 = -0.333(9 + 6x + x2) + 9
0 = (9 * -0.333 + 6x * -0.333 + x2 * -0.333) + 9
0 = (-2.997 + -1.998x + -0.333x2) + 9

Reorder the terms:
0 = -2.997 + 9 + -1.998x + -0.333x2

Combine like terms: -2.997 + 9 = 6.003
0 = 6.003 + -1.998x + -0.333x2

Solving
0 = 6.003 + -1.998x + -0.333x2

Solving for variable 'x'.

Combine like terms: 0 + -6.003 = -6.003
-6.003 + 1.998x + 0.333x2 = 6.003 + -1.998x + -0.333x2 + -6.003 + 1.998x + 0.333x2

Reorder the terms:
-6.003 + 1.998x + 0.333x2 = 6.003 + -6.003 + -1.998x + 1.998x + -0.333x2 + 0.333x2

Combine like terms: 6.003 + -6.003 = 0.000
-6.003 + 1.998x + 0.333x2 = 0.000 + -1.998x + 1.998x + -0.333x2 + 0.333x2
-6.003 + 1.998x + 0.333x2 = -1.998x + 1.998x + -0.333x2 + 0.333x2

Combine like terms: -1.998x + 1.998x = 0.000
-6.003 + 1.998x + 0.333x2 = 0.000 + -0.333x2 + 0.333x2
-6.003 + 1.998x + 0.333x2 = -0.333x2 + 0.333x2

Combine like terms: -0.333x2 + 0.333x2 = 0.000
-6.003 + 1.998x + 0.333x2 = 0.000

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

Divide each side by '0.333'.
-18.02702703 + 6x + x2 = 0

Move the constant term to the right:

Add '18.02702703' to each side of the equation.
-18.02702703 + 6x + 18.02702703 + x2 = 0 + 18.02702703

Reorder the terms:
-18.02702703 + 18.02702703 + 6x + x2 = 0 + 18.02702703

Combine like terms: -18.02702703 + 18.02702703 = 0.00000000
0.00000000 + 6x + x2 = 0 + 18.02702703
6x + x2 = 0 + 18.02702703

Combine like terms: 0 + 18.02702703 = 18.02702703
6x + x2 = 18.02702703

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 = 18.02702703 + 9

Reorder the terms:
9 + 6x + x2 = 18.02702703 + 9

Combine like terms: 18.02702703 + 9 = 27.02702703
9 + 6x + x2 = 27.02702703

Factor a perfect square on the left side:
(x + 3)(x + 3) = 27.02702703

Calculate the square root of the right side: 5.198752449

Break this problem into two subproblems by setting 
(x + 3) equal to 5.198752449 and -5.198752449.

Subproblem 1
x + 3 = 5.198752449

Simplifying
x + 3 = 5.198752449

Reorder the terms:
3 + x = 5.198752449

Solving
3 + x = 5.198752449

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 = 5.198752449 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5.198752449 + -3
x = 5.198752449 + -3

Combine like terms: 5.198752449 + -3 = 2.198752449
x = 2.198752449

Simplifying
x = 2.198752449

Subproblem 2
x + 3 = -5.198752449

Simplifying
x + 3 = -5.198752449

Reorder the terms:
3 + x = -5.198752449

Solving
3 + x = -5.198752449

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 = -5.198752449 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5.198752449 + -3
x = -5.198752449 + -3

Combine like terms: -5.198752449 + -3 = -8.198752449
x = -8.198752449

Simplifying
x = -8.198752449

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.198752449, -8.198752449}