5n^2+27n-18=0

Solution for 5n^2+27n-18=0 equation:

Simplifying
5n2 + 27n + -18 = 0

Reorder the terms:
-18 + 27n + 5n2 = 0

Solving
-18 + 27n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -1n)(3 + -5n) = 0

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

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
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
Solution
n = {-6, 0.6}