n(n+1)=156

Solution for n(n+1)=156 equation:

Simplifying
n(n + 1) = 156

Reorder the terms:
n(1 + n) = 156
(1 * n + n * n) = 156
(1n + n2) = 156

Solving
1n + n2 = 156

Solving for variable 'n'.

Reorder the terms:
-156 + 1n + n2 = 156 + -156

Combine like terms: 156 + -156 = 0
-156 + 1n + n2 = 0

Factor a trinomial.
(-13 + -1n)(12 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -1n)' equal to zero and attempt to solve:

Simplifying
-13 + -1n = 0

Solving
-13 + -1n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1n = 0 + 13
-1n = 0 + 13

Combine like terms: 0 + 13 = 13
-1n = 13

Divide each side by '-1'.
n = -13

Simplifying
n = -13
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

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

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

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-13, 12}