4w(w-6)(w-5)=0

Solution for 4w(w-6)(w-5)=0 equation:

Simplifying
4w(w + -6)(w + -5) = 0

Reorder the terms:
4w(-6 + w)(w + -5) = 0

Reorder the terms:
4w(-6 + w)(-5 + w) = 0

Multiply (-6 + w) * (-5 + w)
4w(-6(-5 + w) + w(-5 + w)) = 0
4w((-5 * -6 + w * -6) + w(-5 + w)) = 0
4w((30 + -6w) + w(-5 + w)) = 0
4w(30 + -6w + (-5 * w + w * w)) = 0
4w(30 + -6w + (-5w + w2)) = 0

Combine like terms: -6w + -5w = -11w
4w(30 + -11w + w2) = 0
(30 * 4w + -11w * 4w + w2 * 4w) = 0
(120w + -44w2 + 4w3) = 0

Solving
120w + -44w2 + 4w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(30 + -11w + w2) = 0

Factor a trinomial.
4w((5 + -1w)(6 + -1w)) = 0

Ignore the factor 4.
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 '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
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, 5, 6}