(4n+2n^3)+(5n^3+2n)=0

Solution for (4n+2n^3)+(5n^3+2n)=0 equation:

Simplifying
(4n + 2n3) + (5n3 + 2n) = 0

Remove parenthesis around (4n + 2n3)
4n + 2n3 + (5n3 + 2n) = 0

Reorder the terms:
4n + 2n3 + (2n + 5n3) = 0

Remove parenthesis around (2n + 5n3)
4n + 2n3 + 2n + 5n3 = 0

Reorder the terms:
4n + 2n + 2n3 + 5n3 = 0

Combine like terms: 4n + 2n = 6n
6n + 2n3 + 5n3 = 0

Combine like terms: 2n3 + 5n3 = 7n3
6n + 7n3 = 0

Solving
6n + 7n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(6 + 7n2) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(6 + 7n2)' equal to zero and attempt to solve:

Simplifying
6 + 7n2 = 0

Solving
6 + 7n2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7n2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7n2 = 0 + -6
7n2 = 0 + -6

Combine like terms: 0 + -6 = -6
7n2 = -6

Divide each side by '7'.
n2 = -0.8571428571

Simplifying
n2 = -0.8571428571

The solution to this equation could not be determined.

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