(w-7)(w-5)20=0

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Solution for (w-7)(w-5)20=0 equation: 


Simplifying
(w + -7)(w + -5) * 20 = 0

Reorder the terms:
(-7 + w)(w + -5) * 20 = 0

Reorder the terms:
(-7 + w)(-5 + w) * 20 = 0

Reorder the terms for easier multiplication:
20(-7 + w)(-5 + w) = 0

Multiply (-7 + w) * (-5 + w)
20(-7(-5 + w) + w(-5 + w)) = 0
20((-5 * -7 + w * -7) + w(-5 + w)) = 0
20((35 + -7w) + w(-5 + w)) = 0
20(35 + -7w + (-5 * w + w * w)) = 0
20(35 + -7w + (-5w + w2)) = 0

Combine like terms: -7w + -5w = -12w
20(35 + -12w + w2) = 0
(35 * 20 + -12w * 20 + w2 * 20) = 0
(700 + -240w + 20w2) = 0

Solving
700 + -240w + 20w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '20'.
20(35 + -12w + w2) = 0

Factor a trinomial.
20((5 + -1w)(7 + -1w)) = 0

Ignore the factor 20.

Subproblem 1
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 2
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
Solution
w = {5, 7}

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