(3v-2)(6+v)=0

Solution for (3v-2)(6+v)=0 equation:

Simplifying
(3v + -2)(6 + v) = 0

Reorder the terms:
(-2 + 3v)(6 + v) = 0

Multiply (-2 + 3v) * (6 + v)
(-2(6 + v) + 3v * (6 + v)) = 0
((6 * -2 + v * -2) + 3v * (6 + v)) = 0
((-12 + -2v) + 3v * (6 + v)) = 0
(-12 + -2v + (6 * 3v + v * 3v)) = 0
(-12 + -2v + (18v + 3v2)) = 0

Combine like terms: -2v + 18v = 16v
(-12 + 16v + 3v2) = 0

Solving
-12 + 16v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-6 + -1v)(2 + -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 '(2 + -3v)' equal to zero and attempt to solve:

Simplifying
2 + -3v = 0

Solving
2 + -3v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3v = 0 + -2
-3v = 0 + -2

Combine like terms: 0 + -2 = -2
-3v = -2

Divide each side by '-3'.
v = 0.6666666667

Simplifying
v = 0.6666666667
Solution
v = {-6, 0.6666666667}