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

Solution for (1+v)(2v-9)=0 equation:

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

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

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

Combine like terms: 2v + -9v = -7v
(-9 + -7v + 2v2) = 0

Solving
-9 + -7v + 2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-1 + -1v)(9 + -2v) = 0

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

Simplifying
-1 + -1v = 0

Solving
-1 + -1v = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1v = 0 + 1
-1v = 0 + 1

Combine like terms: 0 + 1 = 1
-1v = 1

Divide each side by '-1'.
v = -1

Simplifying
v = -1
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 = {-1, 4.5}