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

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

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

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

Multiply (-9 + 2v) * (6 + v)
(-9(6 + v) + 2v * (6 + v)) = 0
((6 * -9 + v * -9) + 2v * (6 + v)) = 0
((-54 + -9v) + 2v * (6 + v)) = 0
(-54 + -9v + (6 * 2v + v * 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}