(n^2)=(3n+18)

Solution for (n^2)=(3n+18) equation:

Simplifying
(n2) = (3n + 18)
n2 = (3n + 18)

Reorder the terms:
n2 = (18 + 3n)

Remove parenthesis around (18 + 3n)
n2 = 18 + 3n

Solving
n2 = 18 + 3n

Solving for variable 'n'.

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

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

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

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

Factor a trinomial.
(-3 + -1n)(6 + -1n) = 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 + -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
Solution
n = {-3, 6}