0=-n^2+14n-48

Solution for 0=-n^2+14n-48 equation:

Simplifying
0 = -1n2 + 14n + -48

Reorder the terms:
0 = -48 + 14n + -1n2

Solving
0 = -48 + 14n + -1n2

Solving for variable 'n'.

Combine like terms: 0 + 48 = 48
48 + -14n + n2 = -48 + 14n + -1n2 + 48 + -14n + n2

Reorder the terms:
48 + -14n + n2 = -48 + 48 + 14n + -14n + -1n2 + n2

Combine like terms: -48 + 48 = 0
48 + -14n + n2 = 0 + 14n + -14n + -1n2 + n2
48 + -14n + n2 = 14n + -14n + -1n2 + n2

Combine like terms: 14n + -14n = 0
48 + -14n + n2 = 0 + -1n2 + n2
48 + -14n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
48 + -14n + n2 = 0

Factor a trinomial.
(6 + -1n)(8 + -1n) = 0

Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
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 = {6, 8}