3y^2-3u^4y^2=0

Solution for 3y^2-3u^4y^2=0 equation:

Simplifying
3y2 + -3u4y2 = 0

Reorder the terms:
-3u4y2 + 3y2 = 0

Solving
-3u4y2 + 3y2 = 0

Solving for variable 'u'.

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

Add '-3y2' to each side of the equation.
-3u4y2 + 3y2 + -3y2 = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-3u4y2 + 0 = 0 + -3y2
-3u4y2 = 0 + -3y2
Remove the zero:
-3u4y2 = -3y2

Divide each side by '-3y2'.
u4 = 1

Simplifying
u4 = 1

Reorder the terms:
-1 + u4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + u4 = 0

Factor a difference between two squares.
(1 + u2)(-1 + u2) = 0

Factor a difference between two squares.
(1 + u2)((1 + u)(-1 + u)) = 0

Subproblem 1
Set the factor '(1 + u2)' equal to zero and attempt to solve:

Simplifying
1 + u2 = 0

Solving
1 + u2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + u2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + u2 = 0 + -1
u2 = 0 + -1

Combine like terms: 0 + -1 = -1
u2 = -1

Simplifying
u2 = -1

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 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

Solving
1 + u = 0

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

Add '-1' to each side of the equation.
1 + -1 + u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + u = 0 + -1
u = 0 + -1

Combine like terms: 0 + -1 = -1
u = -1

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

Simplifying
-1 + u = 0

Solving
-1 + u = 0

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

Add '1' to each side of the equation.
-1 + 1 + u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + u = 0 + 1
u = 0 + 1

Combine like terms: 0 + 1 = 1
u = 1

Simplifying
u = 1
Solution
u = {-1, 1}