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

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Solution for (3v+1)(7-v)=0 equation: 


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

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

Multiply (1 + 3v) * (7 + -1v)
(1(7 + -1v) + 3v * (7 + -1v)) = 0
((7 * 1 + -1v * 1) + 3v * (7 + -1v)) = 0
((7 + -1v) + 3v * (7 + -1v)) = 0
(7 + -1v + (7 * 3v + -1v * 3v)) = 0
(7 + -1v + (21v + -3v2)) = 0

Combine like terms: -1v + 21v = 20v
(7 + 20v + -3v2) = 0

Solving
7 + 20v + -3v2 = 0

Solving for variable 'v'.

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


Subproblem 1
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 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 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7

Subproblem 2
Set the factor '(1 + 3v)' equal to zero and attempt to solve:

Simplifying
1 + 3v = 0

Solving
1 + 3v = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3v = 0 + -1
3v = 0 + -1

Combine like terms: 0 + -1 = -1
3v = -1

Divide each side by '3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Solution
v = {7, -0.3333333333}

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