a^4-2a^2-15=0

Solution for a^4-2a^2-15=0 equation:

Simplifying
a4 + -2a2 + -15 = 0

Reorder the terms:
-15 + -2a2 + a4 = 0

Solving
-15 + -2a2 + a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a2)(5 + -1a2) = 0

Subproblem 1
Set the factor '(-3 + -1a2)' equal to zero and attempt to solve:

Simplifying
-3 + -1a2 = 0

Solving
-3 + -1a2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a2 = 0 + 3
-1a2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1a2 = 3

Divide each side by '-1'.
a2 = -3

Simplifying
a2 = -3

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 '(5 + -1a2)' equal to zero and attempt to solve:

Simplifying
5 + -1a2 = 0

Solving
5 + -1a2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a2 = 0 + -5
-1a2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1a2 = -5

Divide each side by '-1'.
a2 = 5

Simplifying
a2 = 5

Take the square root of each side:
a = {-2.236067978, 2.236067978}
Solution
a = {-2.236067978, 2.236067978}