3n(8n^2-2n+3)=0

Solution for 3n(8n^2-2n+3)=0 equation:

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

Reorder the terms:
3n(3 + -2n + 8n2) = 0
(3 * 3n + -2n * 3n + 8n2 * 3n) = 0
(9n + -6n2 + 24n3) = 0

Solving
9n + -6n2 + 24n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n'.
3n(3 + -2n + 8n2) = 0

Ignore the factor 3.
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 '(3 + -2n + 8n2)' equal to zero and attempt to solve:

Simplifying
3 + -2n + 8n2 = 0

Solving
3 + -2n + 8n2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.375 + -0.25n + n2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -0.25n + -0.375 + n2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -0.25n + n2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -0.25n + n2 = 0 + -0.375
-0.25n + n2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-0.25n + n2 = -0.375

The n term is -0.25n.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25n + 0.015625 + n2 = -0.375 + 0.015625

Reorder the terms:
0.015625 + -0.25n + n2 = -0.375 + 0.015625

Combine like terms: -0.375 + 0.015625 = -0.359375
0.015625 + -0.25n + n2 = -0.359375

Factor a perfect square on the left side:
(n + -0.125)(n + -0.125) = -0.359375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}