5w(w-6)(w+2)=0

Solution for 5w(w-6)(w+2)=0 equation:

Simplifying
5w(w + -6)(w + 2) = 0

Reorder the terms:
5w(-6 + w)(w + 2) = 0

Reorder the terms:
5w(-6 + w)(2 + w) = 0

Multiply (-6 + w) * (2 + w)
5w(-6(2 + w) + w(2 + w)) = 0
5w((2 * -6 + w * -6) + w(2 + w)) = 0
5w((-12 + -6w) + w(2 + w)) = 0
5w(-12 + -6w + (2 * w + w * w)) = 0
5w(-12 + -6w + (2w + w2)) = 0

Combine like terms: -6w + 2w = -4w
5w(-12 + -4w + w2) = 0
(-12 * 5w + -4w * 5w + w2 * 5w) = 0
(-60w + -20w2 + 5w3) = 0

Solving
-60w + -20w2 + 5w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w'.
5w(-12 + -4w + w2) = 0

Factor a trinomial.
5w((-2 + -1w)(6 + -1w)) = 0

Ignore the factor 5.
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 '(-2 + -1w)' equal to zero and attempt to solve:

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

Simplifying
w = -2
Subproblem 3
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {0, -2, 6}