8n^2+8n=160

Solution for 8n^2+8n=160 equation:

Simplifying
8n2 + 8n = 160

Reorder the terms:
8n + 8n2 = 160

Solving
8n + 8n2 = 160

Solving for variable 'n'.

Reorder the terms:
-160 + 8n + 8n2 = 160 + -160

Combine like terms: 160 + -160 = 0
-160 + 8n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-20 + n + n2) = 0

Factor a trinomial.
8((-5 + -1n)(4 + -1n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

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

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

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-5, 4}