5x^5+10x^3+16x=0

Solution for 5x^5+10x^3+16x=0 equation:

Simplifying
5x5 + 10x3 + 16x = 0

Reorder the terms:
16x + 10x3 + 5x5 = 0

Solving
16x + 10x3 + 5x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + 10x2 + 5x4) = 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 '(16 + 10x2 + 5x4)' equal to zero and attempt to solve:

Simplifying
16 + 10x2 + 5x4 = 0

Solving
16 + 10x2 + 5x4 = 0

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

Divide each side by '5'.
3.2 + 2x2 + x4 = 0

Move the constant term to the right:

Add '-3.2' to each side of the equation.
3.2 + 2x2 + -3.2 + x4 = 0 + -3.2

Reorder the terms:
3.2 + -3.2 + 2x2 + x4 = 0 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + 2x2 + x4 = 0 + -3.2
2x2 + x4 = 0 + -3.2

Combine like terms: 0 + -3.2 = -3.2
2x2 + x4 = -3.2

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 = -3.2 + 1

Reorder the terms:
1 + 2x2 + x4 = -3.2 + 1

Combine like terms: -3.2 + 1 = -2.2
1 + 2x2 + x4 = -2.2

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -2.2

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}