72n^2-90n+27=0

Solution for 72n^2-90n+27=0 equation:

Simplifying
72n2 + -90n + 27 = 0

Reorder the terms:
27 + -90n + 72n2 = 0

Solving
27 + -90n + 72n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '9'.
9(3 + -10n + 8n2) = 0

Factor a trinomial.
9((1 + -2n)(3 + -4n)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {0.5, 0.75}