8n^2+2n-210=0

Solution for 8n^2+2n-210=0 equation:

Simplifying
8n2 + 2n + -210 = 0

Reorder the terms:
-210 + 2n + 8n2 = 0

Solving
-210 + 2n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-105 + n + 4n2) = 0

Factor a trinomial.
2((-21 + -4n)(5 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -4n)' equal to zero and attempt to solve:

Simplifying
-21 + -4n = 0

Solving
-21 + -4n = 0

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

Add '21' to each side of the equation.
-21 + 21 + -4n = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -4n = 0 + 21
-4n = 0 + 21

Combine like terms: 0 + 21 = 21
-4n = 21

Divide each side by '-4'.
n = -5.25

Simplifying
n = -5.25
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 = {-5.25, 5}