n^2+3=-4n

Solution for n^2+3=-4n equation:

Simplifying
n2 + 3 = -4n

Reorder the terms:
3 + n2 = -4n

Solving
3 + n2 = -4n

Solving for variable 'n'.

Reorder the terms:
3 + 4n + n2 = -4n + 4n

Combine like terms: -4n + 4n = 0
3 + 4n + n2 = 0

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

Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

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

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

Simplifying
n = -3
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 = {-3, -1}