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

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

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

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

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

Combine like terms: 12v + -6v = 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}