y^4=4y^2

Solution for y^4=4y^2 equation:

Simplifying
y4 = 4y2

Solving
y4 = 4y2

Solving for variable 'y'.

Reorder the terms:
-4y2 + y4 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-4y2 + y4 = 0

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

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

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

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Subproblem 3
Set the factor '(-2 + y)' equal to zero and attempt to solve:

Simplifying
-2 + y = 0

Solving
-2 + y = 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 + y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + y = 0 + 2
y = 0 + 2

Combine like terms: 0 + 2 = 2
y = 2

Simplifying
y = 2
Solution
y = {0, -2, 2}