w^4-21w^2-100=0

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

Simplifying
w4 + -21w2 + -100 = 0

Reorder the terms:
-100 + -21w2 + w4 = 0

Solving
-100 + -21w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + -1w2)(25 + -1w2) = 0

Factor a difference between two squares.
(-4 + -1w2)((5 + w)(5 + -1w)) = 0

Subproblem 1
Set the factor '(-4 + -1w2)' equal to zero and attempt to solve:

Simplifying
-4 + -1w2 = 0

Solving
-4 + -1w2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w2 = 0 + 4
-1w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1w2 = 4

Divide each side by '-1'.
w2 = -4

Simplifying
w2 = -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 '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

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

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Subproblem 3
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-5, 5}