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

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


Simplifying
y4 + -21y2 + -100 = 0

Reorder the terms:
-100 + -21y2 + y4 = 0

Solving
-100 + -21y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y2)(25 + -1y2) = 0

Factor a difference between two squares.
(-4 + -1y2)((5 + y)(5 + -1y)) = 0


Subproblem 1
Set the factor '(-4 + -1y2)' equal to zero and attempt to solve:

Simplifying
-4 + -1y2 = 0

Solving
-4 + -1y2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y2 = 0 + 4
-1y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1y2 = 4

Divide each side by '-1'.
y2 = -4

Simplifying
y2 = -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 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

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

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

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

Simplifying
y = -5

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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

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

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

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

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

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

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