v^2=-20-9v

Solution for v^2=-20-9v equation:

Simplifying
v2 = -20 + -9v

Solving
v2 = -20 + -9v

Solving for variable 'v'.

Reorder the terms:
20 + 9v + v2 = -20 + -9v + 20 + 9v

Reorder the terms:
20 + 9v + v2 = -20 + 20 + -9v + 9v

Combine like terms: -20 + 20 = 0
20 + 9v + v2 = 0 + -9v + 9v
20 + 9v + v2 = -9v + 9v

Combine like terms: -9v + 9v = 0
20 + 9v + v2 = 0

Factor a trinomial.
(5 + v)(4 + v) = 0

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

Simplifying
5 + v = 0

Solving
5 + v = 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 + v = 0 + -5

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

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

Simplifying
v = -5
Subproblem 2
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

Add '-4' to each side of the equation.
4 + -4 + v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v = 0 + -4
v = 0 + -4

Combine like terms: 0 + -4 = -4
v = -4

Simplifying
v = -4
Solution
v = {-5, -4}