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

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


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

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

Multiply (7 + 3v) * (5 + -1v)
(7(5 + -1v) + 3v * (5 + -1v)) = 0
((5 * 7 + -1v * 7) + 3v * (5 + -1v)) = 0
((35 + -7v) + 3v * (5 + -1v)) = 0
(35 + -7v + (5 * 3v + -1v * 3v)) = 0
(35 + -7v + (15v + -3v2)) = 0

Combine like terms: -7v + 15v = 8v
(35 + 8v + -3v2) = 0

Solving
35 + 8v + -3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(5 + -1v)(7 + 3v) = 0


Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5

Subproblem 2
Set the factor '(7 + 3v)' equal to zero and attempt to solve:

Simplifying
7 + 3v = 0

Solving
7 + 3v = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3v = 0 + -7

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

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

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

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

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