-4w(w-5)(w-7)=0

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Solution for -4w(w-5)(w-7)=0 equation: 


Simplifying
-4w(w + -5)(w + -7) = 0

Reorder the terms:
-4w(-5 + w)(w + -7) = 0

Reorder the terms:
-4w(-5 + w)(-7 + w) = 0

Multiply (-5 + w) * (-7 + w)
-4w(-5(-7 + w) + w(-7 + w)) = 0
-4w((-7 * -5 + w * -5) + w(-7 + w)) = 0
-4w((35 + -5w) + w(-7 + w)) = 0
-4w(35 + -5w + (-7 * w + w * w)) = 0
-4w(35 + -5w + (-7w + w2)) = 0

Combine like terms: -5w + -7w = -12w
-4w(35 + -12w + w2) = 0
(35 * -4w + -12w * -4w + w2 * -4w) = 0
(-140w + 48w2 + -4w3) = 0

Solving
-140w + 48w2 + -4w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(-35 + 12w + -1w2) = 0

Factor a trinomial.
4w((-7 + w)(5 + -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 '(-7 + w)' equal to zero and attempt to solve:

Simplifying
-7 + w = 0

Solving
-7 + w = 0

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

Add '7' to each side of the equation.
-7 + 7 + w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + w = 0 + 7
w = 0 + 7

Combine like terms: 0 + 7 = 7
w = 7

Simplifying
w = 7

Subproblem 3
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
Solution
w = {0, 7, 5}

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