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

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

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

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

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

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

Solving
3 + 5v + -2v2 = 0

Solving for variable 'v'.

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

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

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Subproblem 2
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
Solution
v = {3, -0.5}