5n^2+12n-81=0

Solution for 5n^2+12n-81=0 equation:

Simplifying
5n2 + 12n + -81 = 0

Reorder the terms:
-81 + 12n + 5n2 = 0

Solving
-81 + 12n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-27 + -5n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-27 + -5n)' equal to zero and attempt to solve:

Simplifying
-27 + -5n = 0

Solving
-27 + -5n = 0

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

Add '27' to each side of the equation.
-27 + 27 + -5n = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -5n = 0 + 27
-5n = 0 + 27

Combine like terms: 0 + 27 = 27
-5n = 27

Divide each side by '-5'.
n = -5.4

Simplifying
n = -5.4
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 = {-5.4, 3}