b^4+21b^2-100=0

Solution for b^4+21b^2-100=0 equation:

Simplifying
b4 + 21b2 + -100 = 0

Reorder the terms:
-100 + 21b2 + b4 = 0

Solving
-100 + 21b2 + b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(-25 + -1b2)(4 + -1b2) = 0

Factor a difference between two squares.
(-25 + -1b2)((2 + b)(2 + -1b)) = 0

Subproblem 1
Set the factor '(-25 + -1b2)' equal to zero and attempt to solve:

Simplifying
-25 + -1b2 = 0

Solving
-25 + -1b2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1b2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1b2 = 0 + 25
-1b2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1b2 = 25

Divide each side by '-1'.
b2 = -25

Simplifying
b2 = -25

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

Simplifying
2 + b = 0

Solving
2 + b = 0

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

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

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

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

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

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

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

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

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

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

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