(3-v)(4v+2)=0

Solution for (3-v)(4v+2)=0 equation:

Simplifying
(3 + -1v)(4v + 2) = 0

Reorder the terms:
(3 + -1v)(2 + 4v) = 0

Multiply (3 + -1v) * (2 + 4v)
(3(2 + 4v) + -1v * (2 + 4v)) = 0
((2 * 3 + 4v * 3) + -1v * (2 + 4v)) = 0
((6 + 12v) + -1v * (2 + 4v)) = 0
(6 + 12v + (2 * -1v + 4v * -1v)) = 0
(6 + 12v + (-2v + -4v2)) = 0

Combine like terms: 12v + -2v = 10v
(6 + 10v + -4v2) = 0

Solving
6 + 10v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5v + -2v2) = 0

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

Ignore the factor 2.
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}