n(n+1)+n=80

Solution for n(n+1)+n=80 equation:

Simplifying
n(n + 1) + n = 80

Reorder the terms:
n(1 + n) + n = 80
(1 * n + n * n) + n = 80
(1n + n2) + n = 80

Reorder the terms:
1n + n + n2 = 80

Combine like terms: 1n + n = 2n
2n + n2 = 80

Solving
2n + n2 = 80

Solving for variable 'n'.

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

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

Factor a trinomial.
(-10 + -1n)(8 + -1n) = 0

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

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 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 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-10, 8}