18n^2-39n+8=-10

Solution for 18n^2-39n+8=-10 equation:

Simplifying
18n2 + -39n + 8 = -10

Reorder the terms:
8 + -39n + 18n2 = -10

Solving
8 + -39n + 18n2 = -10

Solving for variable 'n'.

Reorder the terms:
8 + 10 + -39n + 18n2 = -10 + 10

Combine like terms: 8 + 10 = 18
18 + -39n + 18n2 = -10 + 10

Combine like terms: -10 + 10 = 0
18 + -39n + 18n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -13n + 6n2) = 0

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

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

Simplifying
2 + -3n = 0

Solving
2 + -3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3n = 0 + -2

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

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

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
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 = {0.6666666667, 1.5}