-4w(w-5)(w-2)=0

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Solution for -4w(w-5)(w-2)=0 equation: 


Simplifying
-4w(w + -5)(w + -2) = 0

Reorder the terms:
-4w(-5 + w)(w + -2) = 0

Reorder the terms:
-4w(-5 + w)(-2 + w) = 0

Multiply (-5 + w) * (-2 + w)
-4w(-5(-2 + w) + w(-2 + w)) = 0
-4w((-2 * -5 + w * -5) + w(-2 + w)) = 0
-4w((10 + -5w) + w(-2 + w)) = 0
-4w(10 + -5w + (-2 * w + w * w)) = 0
-4w(10 + -5w + (-2w + w2)) = 0

Combine like terms: -5w + -2w = -7w
-4w(10 + -7w + w2) = 0
(10 * -4w + -7w * -4w + w2 * -4w) = 0
(-40w + 28w2 + -4w3) = 0

Solving
-40w + 28w2 + -4w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(-10 + 7w + -1w2) = 0

Factor a trinomial.
4w((-5 + w)(2 + -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 + w)' equal to zero and attempt to solve:

Simplifying
-5 + w = 0

Solving
-5 + w = 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 + w = 0 + 5

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

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

Simplifying
w = 5

Subproblem 3
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
Solution
w = {0, 5, 2}

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