66=n(n-5)

Solution for 66=n(n-5) equation:

Simplifying
66 = n(n + -5)

Reorder the terms:
66 = n(-5 + n)
66 = (-5 * n + n * n)
66 = (-5n + n2)

Solving
66 = -5n + n2

Solving for variable 'n'.

Reorder the terms:
66 + 5n + -1n2 = -5n + 5n + n2 + -1n2

Combine like terms: -5n + 5n = 0
66 + 5n + -1n2 = 0 + n2 + -1n2
66 + 5n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
66 + 5n + -1n2 = 0

Factor a trinomial.
(11 + -1n)(6 + n) = 0

Subproblem 1
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Subproblem 2
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

Simplifying
n = -6
Solution
n = {11, -6}