(6+v)(3v+4)=0

Solution for (6+v)(3v+4)=0 equation:

Simplifying
(6 + v)(3v + 4) = 0

Reorder the terms:
(6 + v)(4 + 3v) = 0

Multiply (6 + v) * (4 + 3v)
(6(4 + 3v) + v(4 + 3v)) = 0
((4 * 6 + 3v * 6) + v(4 + 3v)) = 0
((24 + 18v) + v(4 + 3v)) = 0
(24 + 18v + (4 * v + 3v * v)) = 0
(24 + 18v + (4v + 3v2)) = 0

Combine like terms: 18v + 4v = 22v
(24 + 22v + 3v2) = 0

Solving
24 + 22v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + v)(4 + 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 '(4 + 3v)' equal to zero and attempt to solve:

Simplifying
4 + 3v = 0

Solving
4 + 3v = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3v = 0 + -4
3v = 0 + -4

Combine like terms: 0 + -4 = -4
3v = -4

Divide each side by '3'.
v = -1.333333333

Simplifying
v = -1.333333333
Solution
v = {-6, -1.333333333}