n(n+1)+(n+1)=

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

Simplifying
n(n + 1) + (n + 1) = 0

Reorder the terms:
n(1 + n) + (n + 1) = 0
(1 * n + n * n) + (n + 1) = 0
(1n + n2) + (n + 1) = 0

Reorder the terms:
1n + n2 + (1 + n) = 0

Remove parenthesis around (1 + n)
1n + n2 + 1 + n = 0

Reorder the terms:
1 + 1n + n + n2 = 0

Combine like terms: 1n + n = 2n
1 + 2n + n2 = 0

Solving
1 + 2n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + n)(1 + n) = 0

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-1, -1}