-v^2+12=-2v^2-8v

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

Simplifying
-1v2 + 12 = -2v2 + -8v

Reorder the terms:
12 + -1v2 = -2v2 + -8v

Reorder the terms:
12 + -1v2 = -8v + -2v2

Solving
12 + -1v2 = -8v + -2v2

Solving for variable 'v'.

Reorder the terms:
12 + 8v + -1v2 + 2v2 = -8v + -2v2 + 8v + 2v2

Combine like terms: -1v2 + 2v2 = 1v2
12 + 8v + 1v2 = -8v + -2v2 + 8v + 2v2

Reorder the terms:
12 + 8v + 1v2 = -8v + 8v + -2v2 + 2v2

Combine like terms: -8v + 8v = 0
12 + 8v + 1v2 = 0 + -2v2 + 2v2
12 + 8v + 1v2 = -2v2 + 2v2

Combine like terms: -2v2 + 2v2 = 0
12 + 8v + 1v2 = 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}