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

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

Simplifying
0 = a4 + -2a2 + -15

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

Solving
0 = -15 + -2a2 + a4

Solving for variable 'a'.

Combine like terms: 0 + 15 = 15
15 + 2a2 + -1a4 = -15 + -2a2 + a4 + 15 + 2a2 + -1a4

Reorder the terms:
15 + 2a2 + -1a4 = -15 + 15 + -2a2 + 2a2 + a4 + -1a4

Combine like terms: -15 + 15 = 0
15 + 2a2 + -1a4 = 0 + -2a2 + 2a2 + a4 + -1a4
15 + 2a2 + -1a4 = -2a2 + 2a2 + a4 + -1a4

Combine like terms: -2a2 + 2a2 = 0
15 + 2a2 + -1a4 = 0 + a4 + -1a4
15 + 2a2 + -1a4 = a4 + -1a4

Combine like terms: a4 + -1a4 = 0
15 + 2a2 + -1a4 = 0

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

Subproblem 1
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}
Subproblem 2
Set the factor '(3 + a2)' equal to zero and attempt to solve:

Simplifying
3 + a2 = 0

Solving
3 + a2 = 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 + a2 = 0 + -3

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

Combine like terms: 0 + -3 = -3
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.
Solution
a = {-2.236067978, 2.236067978}