27x^3+27x^2+9x=0

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

Simplifying
27x3 + 27x2 + 9x = 0

Reorder the terms:
9x + 27x2 + 27x3 = 0

Solving
9x + 27x2 + 27x3 = 0

Solving for variable 'x'.

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

Ignore the factor 9.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
1 + 3x + 3x2 = 0

Solving
1 + 3x + 3x2 = 0

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

Divide each side by '3'.
0.3333333333 + x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + x + x2 = 0 + -0.3333333333
x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
x + x2 = -0.3333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = -0.3333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
1.25 + x2 = -0.0833333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.0833333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}