12n^2-18n-54=0

Solution for 12n^2-18n-54=0 equation:

Simplifying
12n2 + -18n + -54 = 0

Reorder the terms:
-54 + -18n + 12n2 = 0

Solving
-54 + -18n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + -3n + 2n2) = 0

Factor a trinomial.
6((-3 + -2n)(3 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve:

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 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 + -2n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2n = 0 + 3
-2n = 0 + 3

Combine like terms: 0 + 3 = 3
-2n = 3

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
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 = {-1.5, 3}