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

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

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

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

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

Combine like terms: -3v + 12v = 9v
(-18 + 9v + 2v2) = 0

Solving
-18 + 9v + 2v2 = 0

Solving for variable 'v'.

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

Simplifying
3 + -2v = 0

Solving
3 + -2v = 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 + -2v = 0 + -3

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

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

Divide each side by '-2'.
v = 1.5

Simplifying
v = 1.5
Solution
v = {-6, 1.5}