72=n^2-n

Solution for 72=n^2-n equation:

Simplifying
72 = n2 + -1n

Reorder the terms:
72 = -1n + n2

Solving
72 = -1n + n2

Solving for variable 'n'.

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {9, -8}