5x^3+9x^2+18x=0

Solution for 5x^3+9x^2+18x=0 equation:

Simplifying
5x3 + 9x2 + 18x = 0

Reorder the terms:
18x + 9x2 + 5x3 = 0

Solving
18x + 9x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(18 + 9x + 5x2) = 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 '(18 + 9x + 5x2)' equal to zero and attempt to solve:

Simplifying
18 + 9x + 5x2 = 0

Solving
18 + 9x + 5x2 = 0

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

Divide each side by '5'.
3.6 + 1.8x + x2 = 0

Move the constant term to the right:

Add '-3.6' to each side of the equation.
3.6 + 1.8x + -3.6 + x2 = 0 + -3.6

Reorder the terms:
3.6 + -3.6 + 1.8x + x2 = 0 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + 1.8x + x2 = 0 + -3.6
1.8x + x2 = 0 + -3.6

Combine like terms: 0 + -3.6 = -3.6
1.8x + x2 = -3.6

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = -3.6 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = -3.6 + 0.81

Combine like terms: -3.6 + 0.81 = -2.79
0.81 + 1.8x + x2 = -2.79

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = -2.79

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}