4x^3+18x^2+24x=0

Solution for 4x^3+18x^2+24x=0 equation:

Simplifying
4x3 + 18x2 + 24x = 0

Reorder the terms:
24x + 18x2 + 4x3 = 0

Solving
24x + 18x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(12 + 9x + 2x2) = 0

Ignore the factor 2.
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 '(12 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
12 + 9x + 2x2 = 0

Solving
12 + 9x + 2x2 = 0

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

Divide each side by '2'.
6 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 4.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 4.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 4.5x + x2 = 0 + -6
4.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
4.5x + x2 = -6

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -6 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -6 + 5.0625

Combine like terms: -6 + 5.0625 = -0.9375
5.0625 + 4.5x + x2 = -0.9375

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = -0.9375

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}