8n^2+8n=48

Solution for 8n^2+8n=48 equation:

Simplifying
8n2 + 8n = 48

Reorder the terms:
8n + 8n2 = 48

Solving
8n + 8n2 = 48

Solving for variable 'n'.

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

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

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + n + n2) = 0

Factor a trinomial.
8((-3 + -1n)(2 + -1n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-3, 2}