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

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

Simplifying
(2 + v)(2v + 3) = 0

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

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

Combine like terms: 4v + 3v = 7v
(6 + 7v + 2v2) = 0

Solving
6 + 7v + 2v2 = 0

Solving for variable 'v'.

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

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}