b^4-96b^2-400=0

Solution for b^4-96b^2-400=0 equation:

Simplifying
b4 + -96b2 + -400 = 0

Reorder the terms:
-400 + -96b2 + b4 = 0

Solving
-400 + -96b2 + b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(-4 + -1b2)(100 + -1b2) = 0

Factor a difference between two squares.
(-4 + -1b2)((10 + b)(10 + -1b)) = 0

Subproblem 1
Set the factor '(-4 + -1b2)' equal to zero and attempt to solve:

Simplifying
-4 + -1b2 = 0

Solving
-4 + -1b2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1b2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b2 = 0 + 4
-1b2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1b2 = 4

Divide each side by '-1'.
b2 = -4

Simplifying
b2 = -4

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

Simplifying
10 + b = 0

Solving
10 + b = 0

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

Add '-10' to each side of the equation.
10 + -10 + b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + b = 0 + -10
b = 0 + -10

Combine like terms: 0 + -10 = -10
b = -10

Simplifying
b = -10
Subproblem 3
Set the factor '(10 + -1b)' equal to zero and attempt to solve:

Simplifying
10 + -1b = 0

Solving
10 + -1b = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1b = 0 + -10
-1b = 0 + -10

Combine like terms: 0 + -10 = -10
-1b = -10

Divide each side by '-1'.
b = 10

Simplifying
b = 10
Solution
b = {-10, 10}