125y^4+45y^2-2=0

Solution for 125y^4+45y^2-2=0 equation:

Simplifying
125y4 + 45y2 + -2 = 0

Reorder the terms:
-2 + 45y2 + 125y4 = 0

Solving
-2 + 45y2 + 125y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -5y2)(1 + -25y2) = 0

Factor a difference between two squares.
(-2 + -5y2)((1 + 5y)(1 + -5y)) = 0

Subproblem 1
Set the factor '(-2 + -5y2)' equal to zero and attempt to solve:

Simplifying
-2 + -5y2 = 0

Solving
-2 + -5y2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5y2 = 0 + 2
-5y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5y2 = 2

Divide each side by '-5'.
y2 = -0.4

Simplifying
y2 = -0.4

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 '(1 + 5y)' equal to zero and attempt to solve:

Simplifying
1 + 5y = 0

Solving
1 + 5y = 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 + 5y = 0 + -1

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

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

Divide each side by '5'.
y = -0.2

Simplifying
y = -0.2
Subproblem 3
Set the factor '(1 + -5y)' equal to zero and attempt to solve:

Simplifying
1 + -5y = 0

Solving
1 + -5y = 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 + -5y = 0 + -1

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

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

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
Solution
y = {-0.2, 0.2}