30n^2-27n-27=0

Solution for 30n^2-27n-27=0 equation:

Simplifying
30n2 + -27n + -27 = 0

Reorder the terms:
-27 + -27n + 30n2 = 0

Solving
-27 + -27n + 30n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -9n + 10n2) = 0

Factor a trinomial.
3((-3 + -5n)(3 + -2n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -5n)' equal to zero and attempt to solve:

Simplifying
-3 + -5n = 0

Solving
-3 + -5n = 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 + -5n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5n = 0 + 3
-5n = 0 + 3

Combine like terms: 0 + 3 = 3
-5n = 3

Divide each side by '-5'.
n = -0.6

Simplifying
n = -0.6
Subproblem 2
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
Solution
n = {-0.6, 1.5}