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

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

Simplifying
(6 + -1v)(2v + 3) = 0

Reorder the terms:
(6 + -1v)(3 + 2v) = 0

Multiply (6 + -1v) * (3 + 2v)
(6(3 + 2v) + -1v * (3 + 2v)) = 0
((3 * 6 + 2v * 6) + -1v * (3 + 2v)) = 0
((18 + 12v) + -1v * (3 + 2v)) = 0
(18 + 12v + (3 * -1v + 2v * -1v)) = 0
(18 + 12v + (-3v + -2v2)) = 0

Combine like terms: 12v + -3v = 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}