v^2=-15-8v

Solution for v^2=-15-8v equation:

Simplifying
v2 = -15 + -8v

Solving
v2 = -15 + -8v

Solving for variable 'v'.

Reorder the terms:
15 + 8v + v2 = -15 + -8v + 15 + 8v

Reorder the terms:
15 + 8v + v2 = -15 + 15 + -8v + 8v

Combine like terms: -15 + 15 = 0
15 + 8v + v2 = 0 + -8v + 8v
15 + 8v + v2 = -8v + 8v

Combine like terms: -8v + 8v = 0
15 + 8v + v2 = 0

Factor a trinomial.
(5 + v)(3 + 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 '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 0

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

Add '-3' to each side of the equation.
3 + -3 + v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + v = 0 + -3
v = 0 + -3

Combine like terms: 0 + -3 = -3
v = -3

Simplifying
v = -3
Solution
v = {-5, -3}