10n^2-20n-80=0

Solution for 10n^2-20n-80=0 equation:

Simplifying
10n2 + -20n + -80 = 0

Reorder the terms:
-80 + -20n + 10n2 = 0

Solving
-80 + -20n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + -2n + n2) = 0

Factor a trinomial.
10((-2 + -1n)(4 + -1n)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

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

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

Divide each side by '-1'.
n = -2

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

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-2, 4}