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 + w2) = 0

Factor a trinomial.
5w((-6 + -1w)(3 + -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 '(-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
Subproblem 3
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
Solution
w = {0, -6, 3}