2n^2=-26n-80

Solution for 2n^2=-26n-80 equation:

Simplifying
2n2 = -26n + -80

Reorder the terms:
2n2 = -80 + -26n

Solving
2n2 = -80 + -26n

Solving for variable 'n'.

Reorder the terms:
80 + 26n + 2n2 = -80 + -26n + 80 + 26n

Reorder the terms:
80 + 26n + 2n2 = -80 + 80 + -26n + 26n

Combine like terms: -80 + 80 = 0
80 + 26n + 2n2 = 0 + -26n + 26n
80 + 26n + 2n2 = -26n + 26n

Combine like terms: -26n + 26n = 0
80 + 26n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + 13n + n2) = 0

Factor a trinomial.
2((8 + n)(5 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

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

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

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

Simplifying
n = -5
Solution
n = {-8, -5}