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.
(-7 + -1n)(8 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-7, 8}