(2v+9)(6-v)=0

Solution for (2v+9)(6-v)=0 equation:

Simplifying
(2v + 9)(6 + -1v) = 0

Reorder the terms:
(9 + 2v)(6 + -1v) = 0

Multiply (9 + 2v) * (6 + -1v)
(9(6 + -1v) + 2v * (6 + -1v)) = 0
((6 * 9 + -1v * 9) + 2v * (6 + -1v)) = 0
((54 + -9v) + 2v * (6 + -1v)) = 0
(54 + -9v + (6 * 2v + -1v * 2v)) = 0
(54 + -9v + (12v + -2v2)) = 0

Combine like terms: -9v + 12v = 3v
(54 + 3v + -2v2) = 0

Solving
54 + 3v + -2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + -1v)(9 + 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 '(9 + 2v)' equal to zero and attempt to solve:

Simplifying
9 + 2v = 0

Solving
9 + 2v = 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 + 2v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2v = 0 + -9
2v = 0 + -9

Combine like terms: 0 + -9 = -9
2v = -9

Divide each side by '2'.
v = -4.5

Simplifying
v = -4.5
Solution
v = {6, -4.5}