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

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

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

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

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

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

Solving
2 + 5v + -3v2 = 0

Solving for variable 'v'.

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

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

Simplifying
2 + -1v = 0

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

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

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

Divide each side by '-1'.
v = 2

Simplifying
v = 2
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 = {2, -0.3333333333}