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

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


Simplifying
(5 + -1w)(2w + 7) = 0

Reorder the terms:
(5 + -1w)(7 + 2w) = 0

Multiply (5 + -1w) * (7 + 2w)
(5(7 + 2w) + -1w * (7 + 2w)) = 0
((7 * 5 + 2w * 5) + -1w * (7 + 2w)) = 0
((35 + 10w) + -1w * (7 + 2w)) = 0
(35 + 10w + (7 * -1w + 2w * -1w)) = 0
(35 + 10w + (-7w + -2w2)) = 0

Combine like terms: 10w + -7w = 3w
(35 + 3w + -2w2) = 0

Solving
35 + 3w + -2w2 = 0

Solving for variable 'w'.

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


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 + 2w)' equal to zero and attempt to solve:

Simplifying
7 + 2w = 0

Solving
7 + 2w = 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 + 2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2w = 0 + -7
2w = 0 + -7

Combine like terms: 0 + -7 = -7
2w = -7

Divide each side by '2'.
w = -3.5

Simplifying
w = -3.5
Solution
w = {5, -3.5}

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