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

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

Simplifying
(4v + 6)(3 + -1v) = 0

Reorder the terms:
(6 + 4v)(3 + -1v) = 0

Multiply (6 + 4v) * (3 + -1v)
(6(3 + -1v) + 4v * (3 + -1v)) = 0
((3 * 6 + -1v * 6) + 4v * (3 + -1v)) = 0
((18 + -6v) + 4v * (3 + -1v)) = 0
(18 + -6v + (3 * 4v + -1v * 4v)) = 0
(18 + -6v + (12v + -4v2)) = 0

Combine like terms: -6v + 12v = 6v
(18 + 6v + -4v2) = 0

Solving
18 + 6v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 3v + -2v2) = 0

Factor a trinomial.
2((3 + -1v)(3 + 2v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
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 = {3, -1.5}