(2v+1)(2v+3)=0

Solution for (2v+1)(2v+3)=0 equation:

Simplifying
(2v + 1)(2v + 3) = 0

Reorder the terms:
(1 + 2v)(2v + 3) = 0

Reorder the terms:
(1 + 2v)(3 + 2v) = 0

Multiply (1 + 2v) * (3 + 2v)
(1(3 + 2v) + 2v * (3 + 2v)) = 0
((3 * 1 + 2v * 1) + 2v * (3 + 2v)) = 0
((3 + 2v) + 2v * (3 + 2v)) = 0
(3 + 2v + (3 * 2v + 2v * 2v)) = 0
(3 + 2v + (6v + 4v2)) = 0

Combine like terms: 2v + 6v = 8v
(3 + 8v + 4v2) = 0

Solving
3 + 8v + 4v2 = 0

Solving for variable 'v'.

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

Subproblem 1
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
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 = {-1.5, -0.5}