8n^2+64=72n

Solution for 8n^2+64=72n equation:

Simplifying
8n2 + 64 = 72n

Reorder the terms:
64 + 8n2 = 72n

Solving
64 + 8n2 = 72n

Solving for variable 'n'.

Reorder the terms:
64 + -72n + 8n2 = 72n + -72n

Combine like terms: 72n + -72n = 0
64 + -72n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(8 + -9n + n2) = 0

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

Ignore the factor 8.
Subproblem 1
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
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 = {1, 8}