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

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

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

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

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

Combine like terms: 12v + 9v = 21v
(54 + 21v + 2v2) = 0

Solving
54 + 21v + 2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + v)(9 + 2v) = 0

Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
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}