3x^5+6x^3+9x=0

Solution for 3x^5+6x^3+9x=0 equation:

Simplifying
3x5 + 6x3 + 9x = 0

Reorder the terms:
9x + 6x3 + 3x5 = 0

Solving
9x + 6x3 + 3x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(3 + 2x2 + x4) = 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 '(3 + 2x2 + x4)' equal to zero and attempt to solve:

Simplifying
3 + 2x2 + x4 = 0

Solving
3 + 2x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2x2 + -3 + x4 = 0 + -3

Reorder the terms:
3 + -3 + 2x2 + x4 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x2 + x4 = 0 + -3
2x2 + x4 = 0 + -3

Combine like terms: 0 + -3 = -3
2x2 + x4 = -3

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = -3 + 1

Reorder the terms:
1 + 2x2 + x4 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + 2x2 + x4 = -2

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -2

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}