N^2+24=-11N

Solution for N^2+24=-11N equation:

Simplifying
N2 + 24 = -11N

Reorder the terms:
24 + N2 = -11N

Solving
24 + N2 = -11N

Solving for variable 'N'.

Reorder the terms:
24 + 11N + N2 = -11N + 11N

Combine like terms: -11N + 11N = 0
24 + 11N + N2 = 0

Factor a trinomial.
(8 + N)(3 + N) = 0

Subproblem 1
Set the factor '(8 + N)' equal to zero and attempt to solve:

Simplifying
8 + N = 0

Solving
8 + N = 0

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

Add '-8' to each side of the equation.
8 + -8 + N = 0 + -8

Combine like terms: 8 + -8 = 0
0 + N = 0 + -8
N = 0 + -8

Combine like terms: 0 + -8 = -8
N = -8

Simplifying
N = -8
Subproblem 2
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
Solution
N = {-8, -3}