n(n-5)=66

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

Simplifying
n(n + -5) = 66

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

Solving
-5n + n2 = 66

Solving for variable 'n'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-6, 11}