210n^2-198n+24=0

Solution for 210n^2-198n+24=0 equation:

Simplifying
210n2 + -198n + 24 = 0

Reorder the terms:
24 + -198n + 210n2 = 0

Solving
24 + -198n + 210n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -33n + 35n2) = 0

Factor a trinomial.
6((1 + -7n)(4 + -5n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -7n)' equal to zero and attempt to solve:

Simplifying
1 + -7n = 0

Solving
1 + -7n = 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 + -7n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7n = 0 + -1
-7n = 0 + -1

Combine like terms: 0 + -1 = -1
-7n = -1

Divide each side by '-7'.
n = 0.1428571429

Simplifying
n = 0.1428571429
Subproblem 2
Set the factor '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Solution
n = {0.1428571429, 0.8}