10n^2=27n-18

Solution for 10n^2=27n-18 equation:

Simplifying
10n2 = 27n + -18

Reorder the terms:
10n2 = -18 + 27n

Solving
10n2 = -18 + 27n

Solving for variable 'n'.

Reorder the terms:
18 + -27n + 10n2 = -18 + 27n + 18 + -27n

Reorder the terms:
18 + -27n + 10n2 = -18 + 18 + 27n + -27n

Combine like terms: -18 + 18 = 0
18 + -27n + 10n2 = 0 + 27n + -27n
18 + -27n + 10n2 = 27n + -27n

Combine like terms: 27n + -27n = 0
18 + -27n + 10n2 = 0

Factor a trinomial.
(6 + -5n)(3 + -2n) = 0

Subproblem 1
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 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 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Subproblem 2
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
Solution
n = {1.2, 1.5}