(2v+7)(3+v)=0

Solution for (2v+7)(3+v)=0 equation:

Simplifying
(2v + 7)(3 + v) = 0

Reorder the terms:
(7 + 2v)(3 + v) = 0

Multiply (7 + 2v) * (3 + v)
(7(3 + v) + 2v * (3 + v)) = 0
((3 * 7 + v * 7) + 2v * (3 + v)) = 0
((21 + 7v) + 2v * (3 + v)) = 0
(21 + 7v + (3 * 2v + v * 2v)) = 0
(21 + 7v + (6v + 2v2)) = 0

Combine like terms: 7v + 6v = 13v
(21 + 13v + 2v2) = 0

Solving
21 + 13v + 2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(7 + 2v)(3 + v) = 0

Subproblem 1
Set the factor '(7 + 2v)' equal to zero and attempt to solve:

Simplifying
7 + 2v = 0

Solving
7 + 2v = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2v = 0 + -7
2v = 0 + -7

Combine like terms: 0 + -7 = -7
2v = -7

Divide each side by '2'.
v = -3.5

Simplifying
v = -3.5
Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

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

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

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

Simplifying
v = -3
Solution
v = {-3.5, -3}