y^4+18y^2-19=0

Solution for y^4+18y^2-19=0 equation:

Simplifying
y4 + 18y2 + -19 = 0

Reorder the terms:
-19 + 18y2 + y4 = 0

Solving
-19 + 18y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-19 + -1y2)(1 + -1y2) = 0

Factor a difference between two squares.
(-19 + -1y2)((1 + y)(1 + -1y)) = 0

Subproblem 1
Set the factor '(-19 + -1y2)' equal to zero and attempt to solve:

Simplifying
-19 + -1y2 = 0

Solving
-19 + -1y2 = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1y2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1y2 = 0 + 19
-1y2 = 0 + 19

Combine like terms: 0 + 19 = 19
-1y2 = 19

Divide each side by '-1'.
y2 = -19

Simplifying
y2 = -19

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 '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-1, 1}