36x^5+16x=-52x^3

Solution for 36x^5+16x=-52x^3 equation:

Simplifying
36x5 + 16x = -52x3

Reorder the terms:
16x + 36x5 = -52x3

Solving
16x + 36x5 = -52x3

Solving for variable 'x'.

Reorder the terms:
16x + 52x3 + 36x5 = -52x3 + 52x3

Combine like terms: -52x3 + 52x3 = 0
16x + 52x3 + 36x5 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(4 + 13x2 + 9x4) = 0

Factor a trinomial.
4x((1 + x2)(4 + 9x2)) = 0

Ignore the factor 4.
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 '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(4 + 9x2)' equal to zero and attempt to solve:

Simplifying
4 + 9x2 = 0

Solving
4 + 9x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + 9x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9x2 = 0 + -4
9x2 = 0 + -4

Combine like terms: 0 + -4 = -4
9x2 = -4

Divide each side by '9'.
x2 = -0.4444444444

Simplifying
x2 = -0.4444444444

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}