12x^3+9x^2+6x=

Solution for 12x^3+9x^2+6x= equation:

Simplifying
12x3 + 9x2 + 6x = 0

Reorder the terms:
6x + 9x2 + 12x3 = 0

Solving
6x + 9x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(2 + 3x + 4x2) = 0

Ignore the factor 3.
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 '(2 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
2 + 3x + 4x2 = 0

Solving
2 + 3x + 4x2 = 0

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

Divide each side by '4'.
0.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.75x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.75x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.75x + x2 = 0 + -0.5
0.75x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.75x + x2 = -0.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -0.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.5 + 0.140625

Combine like terms: -0.5 + 0.140625 = -0.359375
0.140625 + 0.75x + x2 = -0.359375

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = -0.359375

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}