3y^4-5y^2=-2

Solution for 3y^4-5y^2=-2 equation:

Simplifying
3y4 + -5y2 = -2

Reorder the terms:
-5y2 + 3y4 = -2

Solving
-5y2 + 3y4 = -2

Solving for variable 'y'.

Reorder the terms:
2 + -5y2 + 3y4 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -5y2 + 3y4 = 0

Factor a trinomial.
(2 + -3y2)(1 + -1y2) = 0

Factor a difference between two squares.
(2 + -3y2)((1 + y)(1 + -1y)) = 0

Subproblem 1
Set the factor '(2 + -3y2)' equal to zero and attempt to solve:

Simplifying
2 + -3y2 = 0

Solving
2 + -3y2 = 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 + -3y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y2 = 0 + -2
-3y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3y2 = -2

Divide each side by '-3'.
y2 = 0.6666666667

Simplifying
y2 = 0.6666666667

Take the square root of each side:
y = {-0.816496581, 0.816496581}
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 = {-0.816496581, 0.816496581, -1, 1}