2y^4=5y^2-3

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

Simplifying
2y4 = 5y2 + -3

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

Solving
2y4 = -3 + 5y2

Solving for variable 'y'.

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

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

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

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

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

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

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

Simplifying
3 + -2y2 = 0

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

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

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

Divide each side by '-2'.
y2 = 1.5

Simplifying
y2 = 1.5

Take the square root of each side:
y = {-1.224744871, 1.224744871}
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 = {-1.224744871, 1.224744871, -1, 1}