(4v+2)(6+v)=0

Solution for (4v+2)(6+v)=0 equation:

Simplifying
(4v + 2)(6 + v) = 0

Reorder the terms:
(2 + 4v)(6 + v) = 0

Multiply (2 + 4v) * (6 + v)
(2(6 + v) + 4v * (6 + v)) = 0
((6 * 2 + v * 2) + 4v * (6 + v)) = 0
((12 + 2v) + 4v * (6 + v)) = 0
(12 + 2v + (6 * 4v + v * 4v)) = 0
(12 + 2v + (24v + 4v2)) = 0

Combine like terms: 2v + 24v = 26v
(12 + 26v + 4v2) = 0

Solving
12 + 26v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 13v + 2v2) = 0

Factor a trinomial.
2((6 + v)(1 + 2v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
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 = {-6, -0.5}