(4v-9)(3+v)=0

Solution for (4v-9)(3+v)=0 equation:

Simplifying
(4v + -9)(3 + v) = 0

Reorder the terms:
(-9 + 4v)(3 + v) = 0

Multiply (-9 + 4v) * (3 + v)
(-9(3 + v) + 4v * (3 + v)) = 0
((3 * -9 + v * -9) + 4v * (3 + v)) = 0
((-27 + -9v) + 4v * (3 + v)) = 0
(-27 + -9v + (3 * 4v + v * 4v)) = 0
(-27 + -9v + (12v + 4v2)) = 0

Combine like terms: -9v + 12v = 3v
(-27 + 3v + 4v2) = 0

Solving
-27 + 3v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-3 + -1v)(9 + -4v) = 0

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 '(9 + -4v)' equal to zero and attempt to solve:

Simplifying
9 + -4v = 0

Solving
9 + -4v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -4v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4v = 0 + -9
-4v = 0 + -9

Combine like terms: 0 + -9 = -9
-4v = -9

Divide each side by '-4'.
v = 2.25

Simplifying
v = 2.25
Solution
v = {-3, 2.25}