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

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


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

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

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

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

Combine like terms: 7w + -5w = 2w
-4w(-35 + 2w + w2) = 0
(-35 * -4w + 2w * -4w + w2 * -4w) = 0
(140w + -8w2 + -4w3) = 0

Solving
140w + -8w2 + -4w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(35 + -2w + -1w2) = 0

Factor a trinomial.
4w((5 + -1w)(7 + w)) = 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 '(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
Solution
w = {0, 5, -7}

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