8n(n+8)=2(32+4n)

Solution for 8n(n+8)=2(32+4n) equation:

Simplifying
8n(n + 8) = 2(32 + 4n)

Reorder the terms:
8n(8 + n) = 2(32 + 4n)
(8 * 8n + n * 8n) = 2(32 + 4n)
(64n + 8n2) = 2(32 + 4n)
64n + 8n2 = (32 * 2 + 4n * 2)
64n + 8n2 = (64 + 8n)

Solving
64n + 8n2 = 64 + 8n

Solving for variable 'n'.

Reorder the terms:
-64 + 64n + -8n + 8n2 = 64 + 8n + -64 + -8n

Combine like terms: 64n + -8n = 56n
-64 + 56n + 8n2 = 64 + 8n + -64 + -8n

Reorder the terms:
-64 + 56n + 8n2 = 64 + -64 + 8n + -8n

Combine like terms: 64 + -64 = 0
-64 + 56n + 8n2 = 0 + 8n + -8n
-64 + 56n + 8n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-64 + 56n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-8 + 7n + n2) = 0

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {-8, 1}