(2+v)(4v+9)=0

Solution for (2+v)(4v+9)=0 equation:

Simplifying
(2 + v)(4v + 9) = 0

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

Multiply (2 + v) * (9 + 4v)
(2(9 + 4v) + v(9 + 4v)) = 0
((9 * 2 + 4v * 2) + v(9 + 4v)) = 0
((18 + 8v) + v(9 + 4v)) = 0
(18 + 8v + (9 * v + 4v * v)) = 0
(18 + 8v + (9v + 4v2)) = 0

Combine like terms: 8v + 9v = 17v
(18 + 17v + 4v2) = 0

Solving
18 + 17v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(9 + 4v)(2 + v) = 0

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

Simplifying
2 + v = 0

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

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

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

Simplifying
v = -2
Solution
v = {-2.25, -2}