2x^5+14x^3+32x=0

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Solution for 2x^5+14x^3+32x=0 equation: 


Simplifying
2x5 + 14x3 + 32x = 0

Reorder the terms:
32x + 14x3 + 2x5 = 0

Solving
32x + 14x3 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(16 + 7x2 + x4) = 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 '(16 + 7x2 + x4)' equal to zero and attempt to solve:

Simplifying
16 + 7x2 + x4 = 0

Solving
16 + 7x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 7x2 + -16 + x4 = 0 + -16

Reorder the terms:
16 + -16 + 7x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 7x2 + x4 = 0 + -16
7x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16
7x2 + x4 = -16

The x term is 7x2.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x2 + 12.25 + x4 = -16 + 12.25

Reorder the terms:
12.25 + 7x2 + x4 = -16 + 12.25

Combine like terms: -16 + 12.25 = -3.75
12.25 + 7x2 + x4 = -3.75

Factor a perfect square on the left side:
(x2 + 3.5)(x2 + 3.5) = -3.75

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}

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