n(n-6)=27

Solution for n(n-6)=27 equation:

Simplifying
n(n + -6) = 27

Reorder the terms:
n(-6 + n) = 27
(-6 * n + n * n) = 27
(-6n + n2) = 27

Solving
-6n + n2 = 27

Solving for variable 'n'.

Reorder the terms:
-27 + -6n + n2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -6n + n2 = 0

Factor a trinomial.
(-3 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
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 = {-3, 9}