9v=2v^2-5

Solution for 9v=2v^2-5 equation:

Simplifying
9v = 2v2 + -5

Reorder the terms:
9v = -5 + 2v2

Solving
9v = -5 + 2v2

Solving for variable 'v'.

Reorder the terms:
5 + 9v + -2v2 = -5 + 2v2 + 5 + -2v2

Reorder the terms:
5 + 9v + -2v2 = -5 + 5 + 2v2 + -2v2

Combine like terms: -5 + 5 = 0
5 + 9v + -2v2 = 0 + 2v2 + -2v2
5 + 9v + -2v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
5 + 9v + -2v2 = 0

Factor a trinomial.
(5 + -1v)(1 + 2v) = 0

Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Subproblem 2
Set the factor '(1 + 2v)' equal to zero and attempt to solve:

Simplifying
1 + 2v = 0

Solving
1 + 2v = 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 + 2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2v = 0 + -1
2v = 0 + -1

Combine like terms: 0 + -1 = -1
2v = -1

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {5, -0.5}