3y-y^3=0

Solution for 3y-y^3=0 equation:

Simplifying
3y + -1y3 = 0

Solving
3y + -1y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + -1y2) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(3 + -1y2)' equal to zero and attempt to solve:

Simplifying
3 + -1y2 = 0

Solving
3 + -1y2 = 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 + -1y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y2 = 0 + -3
-1y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1y2 = -3

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

Simplifying
y2 = 3

Take the square root of each side:
y = {-1.732050808, 1.732050808}
Solution
y = {0, -1.732050808, 1.732050808}