245n^2-56n-21=0

Solution for 245n^2-56n-21=0 equation:

Simplifying
245n2 + -56n + -21 = 0

Reorder the terms:
-21 + -56n + 245n2 = 0

Solving
-21 + -56n + 245n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + -8n + 35n2) = 0

Factor a trinomial.
7((-1 + -5n)(3 + -7n)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-1 + -5n)' equal to zero and attempt to solve:

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 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 + -5n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5n = 0 + 1
-5n = 0 + 1

Combine like terms: 0 + 1 = 1
-5n = 1

Divide each side by '-5'.
n = -0.2

Simplifying
n = -0.2
Subproblem 2
Set the factor '(3 + -7n)' equal to zero and attempt to solve:

Simplifying
3 + -7n = 0

Solving
3 + -7n = 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 + -7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7n = 0 + -3
-7n = 0 + -3

Combine like terms: 0 + -3 = -3
-7n = -3

Divide each side by '-7'.
n = 0.4285714286

Simplifying
n = 0.4285714286
Solution
n = {-0.2, 0.4285714286}