0=a^4-4a^2-21

Solution for 0=a^4-4a^2-21 equation:

Simplifying
0 = a4 + -4a2 + -21

Reorder the terms:
0 = -21 + -4a2 + a4

Solving
0 = -21 + -4a2 + a4

Solving for variable 'a'.

Combine like terms: 0 + 21 = 21
21 + 4a2 + -1a4 = -21 + -4a2 + a4 + 21 + 4a2 + -1a4

Reorder the terms:
21 + 4a2 + -1a4 = -21 + 21 + -4a2 + 4a2 + a4 + -1a4

Combine like terms: -21 + 21 = 0
21 + 4a2 + -1a4 = 0 + -4a2 + 4a2 + a4 + -1a4
21 + 4a2 + -1a4 = -4a2 + 4a2 + a4 + -1a4

Combine like terms: -4a2 + 4a2 = 0
21 + 4a2 + -1a4 = 0 + a4 + -1a4
21 + 4a2 + -1a4 = a4 + -1a4

Combine like terms: a4 + -1a4 = 0
21 + 4a2 + -1a4 = 0

Factor a trinomial.
(7 + -1a2)(3 + a2) = 0

Subproblem 1
Set the factor '(7 + -1a2)' equal to zero and attempt to solve:

Simplifying
7 + -1a2 = 0

Solving
7 + -1a2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a2 = 0 + -7
-1a2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1a2 = -7

Divide each side by '-1'.
a2 = 7

Simplifying
a2 = 7

Take the square root of each side:
a = {-2.645751311, 2.645751311}
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 = {-2.645751311, 2.645751311}