6n^2-24n-72=0

Solution for 6n^2-24n-72=0 equation:

Simplifying
6n2 + -24n + -72 = 0

Reorder the terms:
-72 + -24n + 6n2 = 0

Solving
-72 + -24n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + -4n + n2) = 0

Factor a trinomial.
6((-2 + -1n)(6 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 2
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
Solution
n = {-2, 6}