27n^2+57n-72=0

Solution for 27n^2+57n-72=0 equation:

Simplifying
27n2 + 57n + -72 = 0

Reorder the terms:
-72 + 57n + 27n2 = 0

Solving
-72 + 57n + 27n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 19n + 9n2) = 0

Factor a trinomial.
3((-3 + -1n)(8 + -9n)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(8 + -9n)' equal to zero and attempt to solve:

Simplifying
8 + -9n = 0

Solving
8 + -9n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -9n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9n = 0 + -8
-9n = 0 + -8

Combine like terms: 0 + -8 = -8
-9n = -8

Divide each side by '-9'.
n = 0.8888888889

Simplifying
n = 0.8888888889
Solution
n = {-3, 0.8888888889}