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

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


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

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

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