6n^2=12n+18

Solution for 6n^2=12n+18 equation:

Simplifying
6n2 = 12n + 18

Reorder the terms:
6n2 = 18 + 12n

Solving
6n2 = 18 + 12n

Solving for variable 'n'.

Reorder the terms:
-18 + -12n + 6n2 = 18 + 12n + -18 + -12n

Reorder the terms:
-18 + -12n + 6n2 = 18 + -18 + 12n + -12n

Combine like terms: 18 + -18 = 0
-18 + -12n + 6n2 = 0 + 12n + -12n
-18 + -12n + 6n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
-18 + -12n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -2n + n2) = 0

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

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
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 = {-1, 3}