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

Solution for 0=x^3+6x^2+9x equation:

Simplifying
0 = x3 + 6x2 + 9x

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

Solving
0 = 9x + 6x2 + x3

Solving for variable 'x'.
Remove the zero:
-9x + -6x2 + -1x3 = 9x + 6x2 + x3 + -9x + -6x2 + -1x3

Reorder the terms:
-9x + -6x2 + -1x3 = 9x + -9x + 6x2 + -6x2 + x3 + -1x3

Combine like terms: 9x + -9x = 0
-9x + -6x2 + -1x3 = 0 + 6x2 + -6x2 + x3 + -1x3
-9x + -6x2 + -1x3 = 6x2 + -6x2 + x3 + -1x3

Combine like terms: 6x2 + -6x2 = 0
-9x + -6x2 + -1x3 = 0 + x3 + -1x3
-9x + -6x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-9x + -6x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(9 + 6x + x2) = 0

Factor a trinomial.
-1x((3 + x)(3 + x)) = 0

Ignore the factor -1.
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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {0, -3, -3}