2n(4n+2)=8n

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

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

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

Solving
4n + 8n2 = 8n

Solving for variable 'n'.

Reorder the terms:
4n + -8n + 8n2 = 8n + -8n

Combine like terms: 4n + -8n = -4n
-4n + 8n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-4n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '4n'.
4n(-1 + 2n) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-1 + 2n)' equal to zero and attempt to solve:

Simplifying
-1 + 2n = 0

Solving
-1 + 2n = 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 + 2n = 0 + 1

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

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

Divide each side by '2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {0, 0.5}