0=n^2+3n-18

Solution for 0=n^2+3n-18 equation:

Simplifying
0 = n2 + 3n + -18

Reorder the terms:
0 = -18 + 3n + n2

Solving
0 = -18 + 3n + n2

Solving for variable 'n'.

Combine like terms: 0 + 18 = 18
18 + -3n + -1n2 = -18 + 3n + n2 + 18 + -3n + -1n2

Reorder the terms:
18 + -3n + -1n2 = -18 + 18 + 3n + -3n + n2 + -1n2

Combine like terms: -18 + 18 = 0
18 + -3n + -1n2 = 0 + 3n + -3n + n2 + -1n2
18 + -3n + -1n2 = 3n + -3n + n2 + -1n2

Combine like terms: 3n + -3n = 0
18 + -3n + -1n2 = 0 + n2 + -1n2
18 + -3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
18 + -3n + -1n2 = 0

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

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 '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

Simplifying
n = -6
Solution
n = {3, -6}