3n(8n^2-2n)=

Solution for 3n(8n^2-2n)= equation:

Simplifying
3n(8n2 + -2n) = 0

Reorder the terms:
3n(-2n + 8n2) = 0
(-2n * 3n + 8n2 * 3n) = 0
(-6n2 + 24n3) = 0

Solving
-6n2 + 24n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n2'.
6n2(-1 + 4n) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(-1 + 4n)' equal to zero and attempt to solve:

Simplifying
-1 + 4n = 0

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

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

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

Divide each side by '4'.
n = 0.25

Simplifying
n = 0.25
Solution
n = {0, 0.25}