2y^4-5y^2+2=0

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

Simplifying
2y4 + -5y2 + 2 = 0

Reorder the terms:
2 + -5y2 + 2y4 = 0

Solving
2 + -5y2 + 2y4 = 0

Solving for variable 'y'.

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

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

Simplifying
1 + -2y2 = 0

Solving
1 + -2y2 = 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 + -2y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y2 = 0 + -1
-2y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2y2 = -1

Divide each side by '-2'.
y2 = 0.5

Simplifying
y2 = 0.5

Take the square root of each side:
y = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(2 + -1y2)' equal to zero and attempt to solve:

Simplifying
2 + -1y2 = 0

Solving
2 + -1y2 = 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 + -1y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y2 = 0 + -2
-1y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1y2 = -2

Divide each side by '-1'.
y2 = 2

Simplifying
y2 = 2

Take the square root of each side:
y = {-1.414213562, 1.414213562}
Solution
y = {-0.707106781, 0.707106781, -1.414213562, 1.414213562}