5y^4-7y^2-24=0

Solution for 5y^4-7y^2-24=0 equation:

Simplifying
5y4 + -7y2 + -24 = 0

Reorder the terms:
-24 + -7y2 + 5y4 = 0

Solving
-24 + -7y2 + 5y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-8 + -5y2)(3 + -1y2) = 0

Subproblem 1
Set the factor '(-8 + -5y2)' equal to zero and attempt to solve:

Simplifying
-8 + -5y2 = 0

Solving
-8 + -5y2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5y2 = 0 + 8
-5y2 = 0 + 8

Combine like terms: 0 + 8 = 8
-5y2 = 8

Divide each side by '-5'.
y2 = -1.6

Simplifying
y2 = -1.6

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 '(3 + -1y2)' equal to zero and attempt to solve:

Simplifying
3 + -1y2 = 0

Solving
3 + -1y2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y2 = 0 + -3
-1y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1y2 = -3

Divide each side by '-1'.
y2 = 3

Simplifying
y2 = 3

Take the square root of each side:
y = {-1.732050808, 1.732050808}
Solution
y = {-1.732050808, 1.732050808}