3x^2+27x+9=0

Solution for 3x^2+27x+9=0 equation:

Simplifying
3x2 + 27x + 9 = 0

Reorder the terms:
9 + 27x + 3x2 = 0

Solving
9 + 27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 9x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 9x + x2 = 0

Solving
3 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 9x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 9x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 9x + x2 = 0 + -3
9x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
9x + x2 = -3

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -3 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -3 + 20.25

Combine like terms: -3 + 20.25 = 17.25
20.25 + 9x + x2 = 17.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.153311931 and -4.153311931.

Subproblem 1
x + 4.5 = 4.153311931

Simplifying
x + 4.5 = 4.153311931

Reorder the terms:
4.5 + x = 4.153311931

Solving
4.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.153311931 + -4.5
x = 4.153311931 + -4.5

Combine like terms: 4.153311931 + -4.5 = -0.346688069
x = -0.346688069

Simplifying
x = -0.346688069

Subproblem 2
x + 4.5 = -4.153311931

Simplifying
x + 4.5 = -4.153311931

Reorder the terms:
4.5 + x = -4.153311931

Solving
4.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.153311931 + -4.5
x = -4.153311931 + -4.5

Combine like terms: -4.153311931 + -4.5 = -8.653311931
x = -8.653311931

Simplifying
x = -8.653311931

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.346688069, -8.653311931}
Solution
x = {-0.346688069, -8.653311931}