a^4-10a^2+21=0

Solution for a^4-10a^2+21=0 equation:

Simplifying
a4 + -10a2 + 21 = 0

Reorder the terms:
21 + -10a2 + a4 = 0

Solving
21 + -10a2 + a4 = 0

Solving for variable 'a'.

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

Take the square root of each side:
a = {-1.732050808, 1.732050808}
Subproblem 2
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}
Solution
a = {-1.732050808, 1.732050808, -2.645751311, 2.645751311}