n(n+1)=n+9

Solution for n(n+1)=n+9 equation:

Simplifying
n(n + 1) = n + 9

Reorder the terms:
n(1 + n) = n + 9
(1 * n + n * n) = n + 9
(1n + n2) = n + 9

Reorder the terms:
1n + n2 = 9 + n

Solving
1n + n2 = 9 + n

Solving for variable 'n'.

Reorder the terms:
-9 + 1n + -1n + n2 = 9 + n + -9 + -1n

Combine like terms: 1n + -1n = 0
-9 + 0 + n2 = 9 + n + -9 + -1n
-9 + n2 = 9 + n + -9 + -1n

Reorder the terms:
-9 + n2 = 9 + -9 + n + -1n

Combine like terms: 9 + -9 = 0
-9 + n2 = 0 + n + -1n
-9 + n2 = n + -1n

Combine like terms: n + -1n = 0
-9 + n2 = 0

Factor a difference between two squares.
(3 + n)(-3 + n) = 0

Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(-3 + n)' equal to zero and attempt to solve:

Simplifying
-3 + n = 0

Solving
-3 + n = 0

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

Add '3' to each side of the equation.
-3 + 3 + n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + n = 0 + 3
n = 0 + 3

Combine like terms: 0 + 3 = 3
n = 3

Simplifying
n = 3
Solution
n = {-3, 3}