(3v+7)(6-v)=0

Solution for (3v+7)(6-v)=0 equation:

Simplifying
(3v + 7)(6 + -1v) = 0

Reorder the terms:
(7 + 3v)(6 + -1v) = 0

Multiply (7 + 3v) * (6 + -1v)
(7(6 + -1v) + 3v * (6 + -1v)) = 0
((6 * 7 + -1v * 7) + 3v * (6 + -1v)) = 0
((42 + -7v) + 3v * (6 + -1v)) = 0
(42 + -7v + (6 * 3v + -1v * 3v)) = 0
(42 + -7v + (18v + -3v2)) = 0

Combine like terms: -7v + 18v = 11v
(42 + 11v + -3v2) = 0

Solving
42 + 11v + -3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + -1v)(7 + 3v) = 0

Subproblem 1
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
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 = {6, -2.333333333}