3x(x+9)=3

Solution for 3x(x+9)=3 equation:

Simplifying
3x(x + 9) = 3

Reorder the terms:
3x(9 + x) = 3
(9 * 3x + x * 3x) = 3
(27x + 3x2) = 3

Solving
27x + 3x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 27x + 3x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 9x + x2) = 0

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

Simplifying
-1 + 9x + x2 = 0

Solving
-1 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 9x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 9x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 9x + x2 = 0 + 1
9x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
9x + x2 = 1

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 = 1 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + 9x + x2 = 21.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
x + 4.5 = 4.609772229

Simplifying
x + 4.5 = 4.609772229

Reorder the terms:
4.5 + x = 4.609772229

Solving
4.5 + x = 4.609772229

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 = 4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.609772229 + -4.5
x = 4.609772229 + -4.5

Combine like terms: 4.609772229 + -4.5 = 0.109772229
x = 0.109772229

Simplifying
x = 0.109772229

Subproblem 2
x + 4.5 = -4.609772229

Simplifying
x + 4.5 = -4.609772229

Reorder the terms:
4.5 + x = -4.609772229

Solving
4.5 + x = -4.609772229

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 = -4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.609772229 + -4.5
x = -4.609772229 + -4.5

Combine like terms: -4.609772229 + -4.5 = -9.109772229
x = -9.109772229

Simplifying
x = -9.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.109772229, -9.109772229}
Solution
x = {0.109772229, -9.109772229}