2n^2=-18+15n

Solution for 2n^2=-18+15n equation:

Simplifying
2n2 = -18 + 15n

Solving
2n2 = -18 + 15n

Solving for variable 'n'.

Reorder the terms:
18 + -15n + 2n2 = -18 + 15n + 18 + -15n

Reorder the terms:
18 + -15n + 2n2 = -18 + 18 + 15n + -15n

Combine like terms: -18 + 18 = 0
18 + -15n + 2n2 = 0 + 15n + -15n
18 + -15n + 2n2 = 15n + -15n

Combine like terms: 15n + -15n = 0
18 + -15n + 2n2 = 0

Factor a trinomial.
(3 + -2n)(6 + -1n) = 0

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

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
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 = {1.5, 6}