(5w-10)(w-7)=0

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Solution for (5w-10)(w-7)=0 equation: 


Simplifying
(5w + -10)(w + -7) = 0

Reorder the terms:
(-10 + 5w)(w + -7) = 0

Reorder the terms:
(-10 + 5w)(-7 + w) = 0

Multiply (-10 + 5w) * (-7 + w)
(-10(-7 + w) + 5w * (-7 + w)) = 0
((-7 * -10 + w * -10) + 5w * (-7 + w)) = 0
((70 + -10w) + 5w * (-7 + w)) = 0
(70 + -10w + (-7 * 5w + w * 5w)) = 0
(70 + -10w + (-35w + 5w2)) = 0

Combine like terms: -10w + -35w = -45w
(70 + -45w + 5w2) = 0

Solving
70 + -45w + 5w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + -9w + w2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2

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 = {2, 7}

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