a^4+2a^2-24=0

Solution for a^4+2a^2-24=0 equation:

Simplifying
a4 + 2a2 + -24 = 0

Reorder the terms:
-24 + 2a2 + a4 = 0

Solving
-24 + 2a2 + a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a2)(4 + -1a2) = 0

Factor a difference between two squares.
(-6 + -1a2)((2 + a)(2 + -1a)) = 0

Subproblem 1
Set the factor '(-6 + -1a2)' equal to zero and attempt to solve:

Simplifying
-6 + -1a2 = 0

Solving
-6 + -1a2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a2 = 0 + 6
-1a2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1a2 = 6

Divide each side by '-1'.
a2 = -6

Simplifying
a2 = -6

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 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

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

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

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

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

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