6x^3+2x^2+27x=

Solution for 6x^3+2x^2+27x= equation:

Simplifying
6x3 + 2x2 + 27x = 0

Reorder the terms:
27x + 2x2 + 6x3 = 0

Solving
27x + 2x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(27 + 2x + 6x2) = 0

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 '(27 + 2x + 6x2)' equal to zero and attempt to solve:

Simplifying
27 + 2x + 6x2 = 0

Solving
27 + 2x + 6x2 = 0

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

Divide each side by '6'.
4.5 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 0.3333333333x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 0.3333333333x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 0.3333333333x + x2 = 0 + -4.5
0.3333333333x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
0.3333333333x + x2 = -4.5

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = -4.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = -4.5 + 0.02777777779

Combine like terms: -4.5 + 0.02777777779 = -4.47222222221
0.02777777779 + 0.3333333333x + x2 = -4.47222222221

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = -4.47222222221

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}