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

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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}

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