21d^4-8d^2-5=0

Solution for 21d^4-8d^2-5=0 equation:

Simplifying
21d4 + -8d2 + -5 = 0

Reorder the terms:
-5 + -8d2 + 21d4 = 0

Solving
-5 + -8d2 + 21d4 = 0

Solving for variable 'd'.

Factor a trinomial.
(-1 + -3d2)(5 + -7d2) = 0

Subproblem 1
Set the factor '(-1 + -3d2)' equal to zero and attempt to solve:

Simplifying
-1 + -3d2 = 0

Solving
-1 + -3d2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3d2 = 0 + 1
-3d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3d2 = 1

Divide each side by '-3'.
d2 = -0.3333333333

Simplifying
d2 = -0.3333333333

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 + -7d2)' equal to zero and attempt to solve:

Simplifying
5 + -7d2 = 0

Solving
5 + -7d2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -7d2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7d2 = 0 + -5
-7d2 = 0 + -5

Combine like terms: 0 + -5 = -5
-7d2 = -5

Divide each side by '-7'.
d2 = 0.7142857143

Simplifying
d2 = 0.7142857143

Take the square root of each side:
d = {-0.845154255, 0.845154255}
Solution
d = {-0.845154255, 0.845154255}