9v^2+23v+14=0

Solution for 9v^2+23v+14=0 equation:

Simplifying
9v2 + 23v + 14 = 0

Reorder the terms:
14 + 23v + 9v2 = 0

Solving
14 + 23v + 9v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(14 + 9v)(1 + v) = 0

Subproblem 1
Set the factor '(14 + 9v)' equal to zero and attempt to solve:

Simplifying
14 + 9v = 0

Solving
14 + 9v = 0

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

Add '-14' to each side of the equation.
14 + -14 + 9v = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 9v = 0 + -14
9v = 0 + -14

Combine like terms: 0 + -14 = -14
9v = -14

Divide each side by '9'.
v = -1.555555556

Simplifying
v = -1.555555556
Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Solution
v = {-1.555555556, -1}