-2w(w-7)(w-5)=0

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Solution for -2w(w-7)(w-5)=0 equation: 


Simplifying
-2w(w + -7)(w + -5) = 0

Reorder the terms:
-2w(-7 + w)(w + -5) = 0

Reorder the terms:
-2w(-7 + w)(-5 + w) = 0

Multiply (-7 + w) * (-5 + w)
-2w(-7(-5 + w) + w(-5 + w)) = 0
-2w((-5 * -7 + w * -7) + w(-5 + w)) = 0
-2w((35 + -7w) + w(-5 + w)) = 0
-2w(35 + -7w + (-5 * w + w * w)) = 0
-2w(35 + -7w + (-5w + w2)) = 0

Combine like terms: -7w + -5w = -12w
-2w(35 + -12w + w2) = 0
(35 * -2w + -12w * -2w + w2 * -2w) = 0
(-70w + 24w2 + -2w3) = 0

Solving
-70w + 24w2 + -2w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(-35 + 12w + -1w2) = 0

Factor a trinomial.
2w((-7 + w)(5 + -1w)) = 0

Ignore the factor 2.

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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