n^4+6n^2-40=0

Solution for n^4+6n^2-40=0 equation:

Simplifying
n4 + 6n2 + -40 = 0

Reorder the terms:
-40 + 6n2 + n4 = 0

Solving
-40 + 6n2 + n4 = 0

Solving for variable 'n'.

Factor a trinomial.
(-10 + -1n2)(4 + -1n2) = 0

Factor a difference between two squares.
(-10 + -1n2)((2 + n)(2 + -1n)) = 0

Subproblem 1
Set the factor '(-10 + -1n2)' equal to zero and attempt to solve:

Simplifying
-10 + -1n2 = 0

Solving
-10 + -1n2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n2 = 0 + 10
-1n2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1n2 = 10

Divide each side by '-1'.
n2 = -10

Simplifying
n2 = -10

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 '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Subproblem 3
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-2, 2}