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

Solution for (2+v)(4v-6)=0 equation:

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

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

Multiply (2 + v) * (-6 + 4v)
(2(-6 + 4v) + v(-6 + 4v)) = 0
((-6 * 2 + 4v * 2) + v(-6 + 4v)) = 0
((-12 + 8v) + v(-6 + 4v)) = 0
(-12 + 8v + (-6 * v + 4v * v)) = 0
(-12 + 8v + (-6v + 4v2)) = 0

Combine like terms: 8v + -6v = 2v
(-12 + 2v + 4v2) = 0

Solving
-12 + 2v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + v + 2v2) = 0

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

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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 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 + -1v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v = 0 + 2
-1v = 0 + 2

Combine like terms: 0 + 2 = 2
-1v = 2

Divide each side by '-1'.
v = -2

Simplifying
v = -2
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 = {-2, 1.5}