(3v+5)(6+v)=0

Solution for (3v+5)(6+v)=0 equation:

Simplifying
(3v + 5)(6 + v) = 0

Reorder the terms:
(5 + 3v)(6 + v) = 0

Multiply (5 + 3v) * (6 + v)
(5(6 + v) + 3v * (6 + v)) = 0
((6 * 5 + v * 5) + 3v * (6 + v)) = 0
((30 + 5v) + 3v * (6 + v)) = 0
(30 + 5v + (6 * 3v + v * 3v)) = 0
(30 + 5v + (18v + 3v2)) = 0

Combine like terms: 5v + 18v = 23v
(30 + 23v + 3v2) = 0

Solving
30 + 23v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + v)(5 + 3v) = 0

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

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

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

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

Simplifying
v = -6
Subproblem 2
Set the factor '(5 + 3v)' equal to zero and attempt to solve:

Simplifying
5 + 3v = 0

Solving
5 + 3v = 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 + 3v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3v = 0 + -5
3v = 0 + -5

Combine like terms: 0 + -5 = -5
3v = -5

Divide each side by '3'.
v = -1.666666667

Simplifying
v = -1.666666667
Solution
v = {-6, -1.666666667}