2n^2+8n-80=10

Solution for 2n^2+8n-80=10 equation:

Simplifying
2n2 + 8n + -80 = 10

Reorder the terms:
-80 + 8n + 2n2 = 10

Solving
-80 + 8n + 2n2 = 10

Solving for variable 'n'.

Reorder the terms:
-80 + -10 + 8n + 2n2 = 10 + -10

Combine like terms: -80 + -10 = -90
-90 + 8n + 2n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-90 + 8n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 4n + n2) = 0

Factor a trinomial.
2((-9 + -1n)(5 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9
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 = {-9, 5}