4n^2+24n-108=0

Solution for 4n^2+24n-108=0 equation:

Simplifying
4n2 + 24n + -108 = 0

Reorder the terms:
-108 + 24n + 4n2 = 0

Solving
-108 + 24n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + 6n + n2) = 0

Factor a trinomial.
4((-9 + -1n)(3 + -1n)) = 0

Ignore the factor 4.
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 '(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
Solution
n = {-9, 3}