y^3-6y=0

Solution for y^3-6y=0 equation:

Simplifying
y3 + -6y = 0

Reorder the terms:
-6y + y3 = 0

Solving
-6y + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-6 + 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 '(-6 + y2)' equal to zero and attempt to solve:

Simplifying
-6 + y2 = 0

Solving
-6 + y2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + y2 = 0 + 6
y2 = 0 + 6

Combine like terms: 0 + 6 = 6
y2 = 6

Simplifying
y2 = 6

Take the square root of each side:
y = {-2.449489743, 2.449489743}
Solution
y = {0, -2.449489743, 2.449489743}