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

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


Simplifying
-4(w + -5)(-1w + -7) = 0

Reorder the terms:
-4(-5 + w)(-1w + -7) = 0

Reorder the terms:
-4(-5 + w)(-7 + -1w) = 0

Multiply (-5 + w) * (-7 + -1w)
-4(-5(-7 + -1w) + w(-7 + -1w)) = 0
-4((-7 * -5 + -1w * -5) + w(-7 + -1w)) = 0
-4((35 + 5w) + w(-7 + -1w)) = 0
-4(35 + 5w + (-7 * w + -1w * w)) = 0
-4(35 + 5w + (-7w + -1w2)) = 0

Combine like terms: 5w + -7w = -2w
-4(35 + -2w + -1w2) = 0
(35 * -4 + -2w * -4 + -1w2 * -4) = 0
(-140 + 8w + 4w2) = 0

Solving
-140 + 8w + 4w2 = 0

Solving for variable 'w'.

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

Factor a trinomial.
4((-7 + -1w)(5 + -1w)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve:

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 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 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7

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
Solution
w = {-7, 5}

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