n(n+1)=56

Solution for n(n+1)=56 equation:

Simplifying
n(n + 1) = 56

Reorder the terms:
n(1 + n) = 56
(1 * n + n * n) = 56
(1n + n2) = 56

Solving
1n + n2 = 56

Solving for variable 'n'.

Reorder the terms:
-56 + 1n + n2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + 1n + n2 = 0

Factor a trinomial.
(-8 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-8, 7}