8n^2-8n-30=0

Solution for 8n^2-8n-30=0 equation:

Simplifying
8n2 + -8n + -30 = 0

Reorder the terms:
-30 + -8n + 8n2 = 0

Solving
-30 + -8n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -4n + 4n2) = 0

Factor a trinomial.
2((-3 + -2n)(5 + -2n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve:

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 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 + -2n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2n = 0 + 3
-2n = 0 + 3

Combine like terms: 0 + 3 = 3
-2n = 3

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
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 = {-1.5, 2.5}