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

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

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

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

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

Multiply (2 + v) * (3 + 7v)
(2(3 + 7v) + v(3 + 7v)) = 0
((3 * 2 + 7v * 2) + v(3 + 7v)) = 0
((6 + 14v) + v(3 + 7v)) = 0
(6 + 14v + (3 * v + 7v * v)) = 0
(6 + 14v + (3v + 7v2)) = 0

Combine like terms: 14v + 3v = 17v
(6 + 17v + 7v2) = 0

Solving
6 + 17v + 7v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(2 + v)(3 + 7v) = 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 + 7v)' equal to zero and attempt to solve:

Simplifying
3 + 7v = 0

Solving
3 + 7v = 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 + 7v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7v = 0 + -3
7v = 0 + -3

Combine like terms: 0 + -3 = -3
7v = -3

Divide each side by '7'.
v = -0.4285714286

Simplifying
v = -0.4285714286
Solution
v = {-2, -0.4285714286}