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

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

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

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

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

Combine like terms: -4v + 18v = 14v
(-24 + 14v + 3v2) = 0

Solving
-24 + 14v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-6 + -1v)(4 + -3v) = 0

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

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 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 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
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}