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

Solution for (6+v)(3v+8)=0 equation:

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

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

Multiply (6 + v) * (8 + 3v)
(6(8 + 3v) + v(8 + 3v)) = 0
((8 * 6 + 3v * 6) + v(8 + 3v)) = 0
((48 + 18v) + v(8 + 3v)) = 0
(48 + 18v + (8 * v + 3v * v)) = 0
(48 + 18v + (8v + 3v2)) = 0

Combine like terms: 18v + 8v = 26v
(48 + 26v + 3v2) = 0

Solving
48 + 26v + 3v2 = 0

Solving for variable 'v'.

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

Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(8 + 3v)' equal to zero and attempt to solve:

Simplifying
8 + 3v = 0

Solving
8 + 3v = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3v = 0 + -8

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

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

Divide each side by '3'.
v = -2.666666667

Simplifying
v = -2.666666667
Solution
v = {-6, -2.666666667}