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

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

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

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

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

Combine like terms: 24v + 3v = 27v
(18 + 27v + 4v2) = 0

Solving
18 + 27v + 4v2 = 0

Solving for variable 'v'.

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

Simplifying
3 + 4v = 0

Solving
3 + 4v = 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 + 4v = 0 + -3

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

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

Divide each side by '4'.
v = -0.75

Simplifying
v = -0.75
Solution
v = {-6, -0.75}