y^3-3y=

Solution for y^3-3y= equation:

Simplifying
y3 + -3y = 0

Reorder the terms:
-3y + y3 = 0

Solving
-3y + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-3 + y2) = 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 + y2)' equal to zero and attempt to solve:

Simplifying
-3 + y2 = 0

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

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

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

Simplifying
y2 = 3

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