(6+v)(3v+2)=0

Solution for (6+v)(3v+2)=0 equation:

Simplifying
(6 + v)(3v + 2) = 0

Reorder the terms:
(6 + v)(2 + 3v) = 0

Multiply (6 + v) * (2 + 3v)
(6(2 + 3v) + v(2 + 3v)) = 0
((2 * 6 + 3v * 6) + v(2 + 3v)) = 0
((12 + 18v) + v(2 + 3v)) = 0
(12 + 18v + (2 * v + 3v * v)) = 0
(12 + 18v + (2v + 3v2)) = 0

Combine like terms: 18v + 2v = 20v
(12 + 20v + 3v2) = 0

Solving
12 + 20v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + v)(2 + 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 '(2 + 3v)' equal to zero and attempt to solve:

Simplifying
2 + 3v = 0

Solving
2 + 3v = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3v = 0 + -2
3v = 0 + -2

Combine like terms: 0 + -2 = -2
3v = -2

Divide each side by '3'.
v = -0.6666666667

Simplifying
v = -0.6666666667
Solution
v = {-6, -0.6666666667}