0.5(6n-4n^3)=

Solution for 0.5(6n-4n^3)= equation:

Simplifying
0.5(6n + -4n3) = 0
(6n * 0.5 + -4n3 * 0.5) = 0
(3n + -2n3) = 0

Solving
3n + -2n3 = 0

Solving for variable 'n'.

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

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 + -2n2)' equal to zero and attempt to solve:

Simplifying
3 + -2n2 = 0

Solving
3 + -2n2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n2 = 0 + -3
-2n2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2n2 = -3

Divide each side by '-2'.
n2 = 1.5

Simplifying
n2 = 1.5

Take the square root of each side:
n = {-1.224744871, 1.224744871}
Solution
n = {0, -1.224744871, 1.224744871}