56=(n-2)(n-3)

Solution for 56=(n-2)(n-3) equation:

Simplifying
56 = (n + -2)(n + -3)

Reorder the terms:
56 = (-2 + n)(n + -3)

Reorder the terms:
56 = (-2 + n)(-3 + n)

Multiply (-2 + n) * (-3 + n)
56 = (-2(-3 + n) + n(-3 + n))
56 = ((-3 * -2 + n * -2) + n(-3 + n))
56 = ((6 + -2n) + n(-3 + n))
56 = (6 + -2n + (-3 * n + n * n))
56 = (6 + -2n + (-3n + n2))

Combine like terms: -2n + -3n = -5n
56 = (6 + -5n + n2)

Solving
56 = 6 + -5n + n2

Solving for variable 'n'.

Combine like terms: 56 + -6 = 50
50 + 5n + -1n2 = 6 + -5n + n2 + -6 + 5n + -1n2

Reorder the terms:
50 + 5n + -1n2 = 6 + -6 + -5n + 5n + n2 + -1n2

Combine like terms: 6 + -6 = 0
50 + 5n + -1n2 = 0 + -5n + 5n + n2 + -1n2
50 + 5n + -1n2 = -5n + 5n + n2 + -1n2

Combine like terms: -5n + 5n = 0
50 + 5n + -1n2 = 0 + n2 + -1n2
50 + 5n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
50 + 5n + -1n2 = 0

Factor a trinomial.
(10 + -1n)(5 + n) = 0

Subproblem 1
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {10, -5}