2q=-q^2-1

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

Simplifying
2q = -1q2 + -1

Reorder the terms:
2q = -1 + -1q2

Solving
2q = -1 + -1q2

Solving for variable 'q'.

Reorder the terms:
1 + 2q + q2 = -1 + -1q2 + 1 + q2

Reorder the terms:
1 + 2q + q2 = -1 + 1 + -1q2 + q2

Combine like terms: -1 + 1 = 0
1 + 2q + q2 = 0 + -1q2 + q2
1 + 2q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
1 + 2q + q2 = 0

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

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

Simplifying
1 + q = 0

Solving
1 + q = 0

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

Add '-1' to each side of the equation.
1 + -1 + q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + q = 0 + -1
q = 0 + -1

Combine like terms: 0 + -1 = -1
q = -1

Simplifying
q = -1
Subproblem 2
Set the factor '(1 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

Solving
1 + q = 0

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

Add '-1' to each side of the equation.
1 + -1 + q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + q = 0 + -1
q = 0 + -1

Combine like terms: 0 + -1 = -1
q = -1

Simplifying
q = -1
Solution
q = {-1, -1}