8n^2-16n-10=0

Solution for 8n^2-16n-10=0 equation:

Simplifying
8n2 + -16n + -10 = 0

Reorder the terms:
-10 + -16n + 8n2 = 0

Solving
-10 + -16n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -8n + 4n2) = 0

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

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

Simplifying
-1 + -2n = 0

Solving
-1 + -2n = 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 + -2n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2n = 0 + 1
-2n = 0 + 1

Combine like terms: 0 + 1 = 1
-2n = 1

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 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 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Solution
n = {-0.5, 2.5}