n(n-3)=108

Solution for n(n-3)=108 equation:

Simplifying
n(n + -3) = 108

Reorder the terms:
n(-3 + n) = 108
(-3 * n + n * n) = 108
(-3n + n2) = 108

Solving
-3n + n2 = 108

Solving for variable 'n'.

Reorder the terms:
-108 + -3n + n2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + -3n + n2 = 0

Factor a trinomial.
(-9 + -1n)(12 + -1n) = 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 '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-9, 12}