0=n^2-8n-48

Solution for 0=n^2-8n-48 equation:

Simplifying
0 = n2 + -8n + -48

Reorder the terms:
0 = -48 + -8n + n2

Solving
0 = -48 + -8n + n2

Solving for variable 'n'.

Combine like terms: 0 + 48 = 48
48 + 8n + -1n2 = -48 + -8n + n2 + 48 + 8n + -1n2

Reorder the terms:
48 + 8n + -1n2 = -48 + 48 + -8n + 8n + n2 + -1n2

Combine like terms: -48 + 48 = 0
48 + 8n + -1n2 = 0 + -8n + 8n + n2 + -1n2
48 + 8n + -1n2 = -8n + 8n + n2 + -1n2

Combine like terms: -8n + 8n = 0
48 + 8n + -1n2 = 0 + n2 + -1n2
48 + 8n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
48 + 8n + -1n2 = 0

Factor a trinomial.
(12 + -1n)(4 + n) = 0

Subproblem 1
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {12, -4}