-5w(w+6)(w-3)=0

Solution for -5w(w+6)(w-3)=0 equation:

Simplifying
-5w(w + 6)(w + -3) = 0

Reorder the terms:
-5w(6 + w)(w + -3) = 0

Reorder the terms:
-5w(6 + w)(-3 + w) = 0

Multiply (6 + w) * (-3 + w)
-5w(6(-3 + w) + w(-3 + w)) = 0
-5w((-3 * 6 + w * 6) + w(-3 + w)) = 0
-5w((-18 + 6w) + w(-3 + w)) = 0
-5w(-18 + 6w + (-3 * w + w * w)) = 0
-5w(-18 + 6w + (-3w + w2)) = 0

Combine like terms: 6w + -3w = 3w
-5w(-18 + 3w + w2) = 0
(-18 * -5w + 3w * -5w + w2 * -5w) = 0
(90w + -15w2 + -5w3) = 0

Solving
90w + -15w2 + -5w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w'.
5w(18 + -3w + -1w2) = 0

Factor a trinomial.
5w((3 + -1w)(6 + w)) = 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 '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

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

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

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

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

Simplifying
6 + w = 0

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

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

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

Simplifying
w = -6
Solution
w = {0, 3, -6}