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

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

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

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

Multiply (6 + 4v) * (2 + v)
(6(2 + v) + 4v * (2 + v)) = 0
((2 * 6 + v * 6) + 4v * (2 + v)) = 0
((12 + 6v) + 4v * (2 + v)) = 0
(12 + 6v + (2 * 4v + v * 4v)) = 0
(12 + 6v + (8v + 4v2)) = 0

Combine like terms: 6v + 8v = 14v
(12 + 14v + 4v2) = 0

Solving
12 + 14v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 7v + 2v2) = 0

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

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

Simplifying
2 + v = 0

Solving
2 + v = 0

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

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + v = 0 + -2
v = 0 + -2

Combine like terms: 0 + -2 = -2
v = -2

Simplifying
v = -2
Subproblem 2
Set the factor '(3 + 2v)' equal to zero and attempt to solve:

Simplifying
3 + 2v = 0

Solving
3 + 2v = 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 + 2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2v = 0 + -3
2v = 0 + -3

Combine like terms: 0 + -3 = -3
2v = -3

Divide each side by '2'.
v = -1.5

Simplifying
v = -1.5
Solution
v = {-2, -1.5}