q^2+2=-3q

Solution for q^2+2=-3q equation:

Simplifying
q2 + 2 = -3q

Reorder the terms:
2 + q2 = -3q

Solving
2 + q2 = -3q

Solving for variable 'q'.

Reorder the terms:
2 + 3q + q2 = -3q + 3q

Combine like terms: -3q + 3q = 0
2 + 3q + q2 = 0

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

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

Simplifying
2 + q = 0

Solving
2 + q = 0

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

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

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

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

Simplifying
q = -2
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 = {-2, -1}