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

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

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

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

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

Combine like terms: 24v + 2v = 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}