v^2=-1-2v

Solution for v^2=-1-2v equation:

Simplifying
v2 = -1 + -2v

Solving
v2 = -1 + -2v

Solving for variable 'v'.

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

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

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

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

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

Subproblem 1
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
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, -1}