n^2=2n+24

Solution for n^2=2n+24 equation:

Simplifying
n2 = 2n + 24

Reorder the terms:
n2 = 24 + 2n

Solving
n2 = 24 + 2n

Solving for variable 'n'.

Reorder the terms:
-24 + -2n + n2 = 24 + 2n + -24 + -2n

Reorder the terms:
-24 + -2n + n2 = 24 + -24 + 2n + -2n

Combine like terms: 24 + -24 = 0
-24 + -2n + n2 = 0 + 2n + -2n
-24 + -2n + n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-24 + -2n + n2 = 0

Factor a trinomial.
(-4 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-4, 6}