2n^4-10n^2-72=0

Solution for 2n^4-10n^2-72=0 equation:

Simplifying
2n4 + -10n2 + -72 = 0

Reorder the terms:
-72 + -10n2 + 2n4 = 0

Solving
-72 + -10n2 + 2n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -5n2 + n4) = 0

Factor a trinomial.
2((-4 + -1n2)(9 + -1n2)) = 0

Factor a difference between two squares.
2((-4 + -1n2)((3 + n)(3 + -1n))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1n2)' equal to zero and attempt to solve:

Simplifying
-4 + -1n2 = 0

Solving
-4 + -1n2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n2 = 0 + 4
-1n2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1n2 = 4

Divide each side by '-1'.
n2 = -4

Simplifying
n2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Subproblem 3
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-3, 3}