n(n+1)=12

Solution for n(n+1)=12 equation:

Simplifying
n(n + 1) = 12

Reorder the terms:
n(1 + n) = 12
(1 * n + n * n) = 12
(1n + n2) = 12

Solving
1n + n2 = 12

Solving for variable 'n'.

Reorder the terms:
-12 + 1n + n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 1n + n2 = 0

Factor a trinomial.
(-4 + -1n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-4, 3}