21n^2-102n-15=0

Solution for 21n^2-102n-15=0 equation:

Simplifying
21n2 + -102n + -15 = 0

Reorder the terms:
-15 + -102n + 21n2 = 0

Solving
-15 + -102n + 21n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -34n + 7n2) = 0

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

Ignore the factor 3.
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 '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

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

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

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-0.1428571429, 5}