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

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

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

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

Multiply (3 + v) * (2 + 3v)
(3(2 + 3v) + v(2 + 3v)) = 0
((2 * 3 + 3v * 3) + v(2 + 3v)) = 0
((6 + 9v) + v(2 + 3v)) = 0
(6 + 9v + (2 * v + 3v * v)) = 0
(6 + 9v + (2v + 3v2)) = 0

Combine like terms: 9v + 2v = 11v
(6 + 11v + 3v2) = 0

Solving
6 + 11v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(3 + v)(2 + 3v) = 0

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

Simplifying
3 + v = 0

Solving
3 + v = 0

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

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

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

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

Simplifying
v = -3
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 = {-3, -0.6666666667}