n^2=-3n-2

Solution for n^2=-3n-2 equation:

Simplifying
n2 = -3n + -2

Reorder the terms:
n2 = -2 + -3n

Solving
n2 = -2 + -3n

Solving for variable 'n'.

Reorder the terms:
2 + 3n + n2 = -2 + -3n + 2 + 3n

Reorder the terms:
2 + 3n + n2 = -2 + 2 + -3n + 3n

Combine like terms: -2 + 2 = 0
2 + 3n + n2 = 0 + -3n + 3n
2 + 3n + n2 = -3n + 3n

Combine like terms: -3n + 3n = 0
2 + 3n + n2 = 0

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

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

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

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

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

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-2, -1}