45n^2-275n+30=0

Solution for 45n^2-275n+30=0 equation:

Simplifying
45n2 + -275n + 30 = 0

Reorder the terms:
30 + -275n + 45n2 = 0

Solving
30 + -275n + 45n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -55n + 9n2) = 0

Factor a trinomial.
5((1 + -9n)(6 + -1n)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -9n)' equal to zero and attempt to solve:

Simplifying
1 + -9n = 0

Solving
1 + -9n = 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 + -9n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9n = 0 + -1
-9n = 0 + -1

Combine like terms: 0 + -1 = -1
-9n = -1

Divide each side by '-9'.
n = 0.1111111111

Simplifying
n = 0.1111111111
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 = {0.1111111111, 6}