n^2=72+n

Solution for n^2=72+n equation:

Simplifying
n2 = 72 + n

Solving
n2 = 72 + n

Solving for variable 'n'.

Reorder the terms:
-72 + -1n + n2 = 72 + n + -72 + -1n

Reorder the terms:
-72 + -1n + n2 = 72 + -72 + n + -1n

Combine like terms: 72 + -72 = 0
-72 + -1n + n2 = 0 + n + -1n
-72 + -1n + n2 = n + -1n

Combine like terms: n + -1n = 0
-72 + -1n + n2 = 0

Factor a trinomial.
(-8 + -1n)(9 + -1n) = 0

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

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 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 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-8, 9}