6n^2+24n=72

Solution for 6n^2+24n=72 equation:

Simplifying
6n2 + 24n = 72

Reorder the terms:
24n + 6n2 = 72

Solving
24n + 6n2 = 72

Solving for variable 'n'.

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

Combine like terms: 72 + -72 = 0
-72 + 24n + 6n2 = 0

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

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

Ignore the factor 6.
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 '(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
Solution
n = {-6, 2}