-2n^2+12n=18

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

Simplifying
-2n2 + 12n = 18

Reorder the terms:
12n + -2n2 = 18

Solving
12n + -2n2 = 18

Solving for variable 'n'.

Reorder the terms:
-18 + 12n + -2n2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 12n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 6n + -1n2) = 0

Factor a trinomial.
2((-3 + n)(3 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + n)' equal to zero and attempt to solve:

Simplifying
-3 + n = 0

Solving
-3 + n = 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 + n = 0 + 3

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

Combine like terms: 0 + 3 = 3
n = 3

Simplifying
n = 3
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 = {3, 3}