y^4+y^2-42=0

Solution for y^4+y^2-42=0 equation:

Simplifying
y4 + y2 + -42 = 0

Reorder the terms:
-42 + y2 + y4 = 0

Solving
-42 + y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -1y2)(6 + -1y2) = 0

Subproblem 1
Set the factor '(-7 + -1y2)' equal to zero and attempt to solve:

Simplifying
-7 + -1y2 = 0

Solving
-7 + -1y2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y2 = 0 + 7
-1y2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1y2 = 7

Divide each side by '-1'.
y2 = -7

Simplifying
y2 = -7

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 '(6 + -1y2)' equal to zero and attempt to solve:

Simplifying
6 + -1y2 = 0

Solving
6 + -1y2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y2 = 0 + -6
-1y2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1y2 = -6

Divide each side by '-1'.
y2 = 6

Simplifying
y2 = 6

Take the square root of each side:
y = {-2.449489743, 2.449489743}
Solution
y = {-2.449489743, 2.449489743}