(3w+7)(5-w)=0

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Solution for (3w+7)(5-w)=0 equation: 


Simplifying
(3w + 7)(5 + -1w) = 0

Reorder the terms:
(7 + 3w)(5 + -1w) = 0

Multiply (7 + 3w) * (5 + -1w)
(7(5 + -1w) + 3w * (5 + -1w)) = 0
((5 * 7 + -1w * 7) + 3w * (5 + -1w)) = 0
((35 + -7w) + 3w * (5 + -1w)) = 0
(35 + -7w + (5 * 3w + -1w * 3w)) = 0
(35 + -7w + (15w + -3w2)) = 0

Combine like terms: -7w + 15w = 8w
(35 + 8w + -3w2) = 0

Solving
35 + 8w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + -1w)(7 + 3w) = 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 + 3w)' equal to zero and attempt to solve:

Simplifying
7 + 3w = 0

Solving
7 + 3w = 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 + 3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3w = 0 + -7
3w = 0 + -7

Combine like terms: 0 + -7 = -7
3w = -7

Divide each side by '3'.
w = -2.333333333

Simplifying
w = -2.333333333
Solution
w = {5, -2.333333333}

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