v^2=-12-8v

Solution for v^2=-12-8v equation:

Simplifying
v2 = -12 + -8v

Solving
v2 = -12 + -8v

Solving for variable 'v'.

Reorder the terms:
12 + 8v + v2 = -12 + -8v + 12 + 8v

Reorder the terms:
12 + 8v + v2 = -12 + 12 + -8v + 8v

Combine like terms: -12 + 12 = 0
12 + 8v + v2 = 0 + -8v + 8v
12 + 8v + v2 = -8v + 8v

Combine like terms: -8v + 8v = 0
12 + 8v + v2 = 0

Factor a trinomial.
(6 + v)(2 + v) = 0

Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(2 + v)' equal to zero and attempt to solve:

Simplifying
2 + v = 0

Solving
2 + v = 0

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

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

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

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

Simplifying
v = -2
Solution
v = {-6, -2}