(3+V)(4V+2)=0

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

Simplifying
(3 + V)(4V + 2) = 0

Reorder the terms:
(3 + V)(2 + 4V) = 0

Multiply (3 + V) * (2 + 4V)
(3(2 + 4V) + V(2 + 4V)) = 0
((2 * 3 + 4V * 3) + V(2 + 4V)) = 0
((6 + 12V) + V(2 + 4V)) = 0
(6 + 12V + (2 * V + 4V * V)) = 0
(6 + 12V + (2V + 4V2)) = 0

Combine like terms: 12V + 2V = 14V
(6 + 14V + 4V2) = 0

Solving
6 + 14V + 4V2 = 0

Solving for variable 'V'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 7V + 2V2) = 0

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

Ignore the factor 2.
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 '(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}