8y^6-38y^4-10y^2=0

Solution for 8y^6-38y^4-10y^2=0 equation:

Simplifying
8y6 + -38y4 + -10y2 = 0

Reorder the terms:
-10y2 + -38y4 + 8y6 = 0

Solving
-10y2 + -38y4 + 8y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y2'.
2y2(-5 + -19y2 + 4y4) = 0

Factor a trinomial.
2y2((-1 + -4y2)(5 + -1y2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(-1 + -4y2)' equal to zero and attempt to solve:

Simplifying
-1 + -4y2 = 0

Solving
-1 + -4y2 = 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 + -4y2 = 0 + 1

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

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

Divide each side by '-4'.
y2 = -0.25

Simplifying
y2 = -0.25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(5 + -1y2)' equal to zero and attempt to solve:

Simplifying
5 + -1y2 = 0

Solving
5 + -1y2 = 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 + -1y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y2 = 0 + -5
-1y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1y2 = -5

Divide each side by '-1'.
y2 = 5

Simplifying
y2 = 5

Take the square root of each side:
y = {-2.236067978, 2.236067978}
Solution
y = {0, -2.236067978, 2.236067978}