(3v+1)(2v+1)=0

Solution for (3v+1)(2v+1)=0 equation:

Simplifying
(3v + 1)(2v + 1) = 0

Reorder the terms:
(1 + 3v)(2v + 1) = 0

Reorder the terms:
(1 + 3v)(1 + 2v) = 0

Multiply (1 + 3v) * (1 + 2v)
(1(1 + 2v) + 3v * (1 + 2v)) = 0
((1 * 1 + 2v * 1) + 3v * (1 + 2v)) = 0
((1 + 2v) + 3v * (1 + 2v)) = 0
(1 + 2v + (1 * 3v + 2v * 3v)) = 0
(1 + 2v + (3v + 6v2)) = 0

Combine like terms: 2v + 3v = 5v
(1 + 5v + 6v2) = 0

Solving
1 + 5v + 6v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(1 + 2v)(1 + 3v) = 0

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

Simplifying
1 + 2v = 0

Solving
1 + 2v = 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 + 2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2v = 0 + -1
2v = 0 + -1

Combine like terms: 0 + -1 = -1
2v = -1

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
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 = {-0.5, -0.3333333333}