w^3-6w=0

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

Simplifying
w3 + -6w = 0

Reorder the terms:
-6w + w3 = 0

Solving
-6w + w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w'.
w(-6 + w2) = 0

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

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(-6 + w2)' equal to zero and attempt to solve:

Simplifying
-6 + w2 = 0

Solving
-6 + w2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + w2 = 0 + 6
w2 = 0 + 6

Combine like terms: 0 + 6 = 6
w2 = 6

Simplifying
w2 = 6

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