3w(w-1)(w+6)=0

Solution for 3w(w-1)(w+6)=0 equation:

Simplifying
3w(w + -1)(w + 6) = 0

Reorder the terms:
3w(-1 + w)(w + 6) = 0

Reorder the terms:
3w(-1 + w)(6 + w) = 0

Multiply (-1 + w) * (6 + w)
3w(-1(6 + w) + w(6 + w)) = 0
3w((6 * -1 + w * -1) + w(6 + w)) = 0
3w((-6 + -1w) + w(6 + w)) = 0
3w(-6 + -1w + (6 * w + w * w)) = 0
3w(-6 + -1w + (6w + w2)) = 0

Combine like terms: -1w + 6w = 5w
3w(-6 + 5w + w2) = 0
(-6 * 3w + 5w * 3w + w2 * 3w) = 0
(-18w + 15w2 + 3w3) = 0

Solving
-18w + 15w2 + 3w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w'.
3w(-6 + 5w + w2) = 0

Factor a trinomial.
3w((-6 + -1w)(1 + -1w)) = 0

Ignore the factor 3.
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 '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Solution
w = {0, -6, 1}