=n^2-n-56

Solution for =n^2-n-56 equation:

Simplifying
0 = n2 + -1n + -56

Reorder the terms:
0 = -56 + -1n + n2

Solving
0 = -56 + -1n + n2

Solving for variable 'n'.

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

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

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

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

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

Factor a trinomial.
(8 + -1n)(7 + n) = 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 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 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 + n = 0 + -7

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

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

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