(8v+3)(v+1)=0

Solution for (8v+3)(v+1)=0 equation:

Simplifying
(8v + 3)(v + 1) = 0

Reorder the terms:
(3 + 8v)(v + 1) = 0

Reorder the terms:
(3 + 8v)(1 + v) = 0

Multiply (3 + 8v) * (1 + v)
(3(1 + v) + 8v * (1 + v)) = 0
((1 * 3 + v * 3) + 8v * (1 + v)) = 0
((3 + 3v) + 8v * (1 + v)) = 0
(3 + 3v + (1 * 8v + v * 8v)) = 0
(3 + 3v + (8v + 8v2)) = 0

Combine like terms: 3v + 8v = 11v
(3 + 11v + 8v2) = 0

Solving
3 + 11v + 8v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(1 + v)(3 + 8v) = 0

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

Simplifying
1 + v = 0

Solving
1 + v = 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 + v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + v = 0 + -1
v = 0 + -1

Combine like terms: 0 + -1 = -1
v = -1

Simplifying
v = -1
Subproblem 2
Set the factor '(3 + 8v)' equal to zero and attempt to solve:

Simplifying
3 + 8v = 0

Solving
3 + 8v = 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 + 8v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8v = 0 + -3
8v = 0 + -3

Combine like terms: 0 + -3 = -3
8v = -3

Divide each side by '8'.
v = -0.375

Simplifying
v = -0.375
Solution
v = {-1, -0.375}