Solving the Equation (5n)(31/2n)(n4) = 0
This equation is a cubic equation, meaning it has a highest power of 3 for the variable 'n'. To solve it, we can use the Zero Product Property, which states that if the product of several factors is zero, then at least one of the factors must be zero.
Applying the Zero Product Property
Let's break down the equation into its individual factors:
 (5  n) = 0
 (3  1/2n) = 0
 (n  4) = 0
Now, we can solve each of these linear equations individually:

5  n = 0
 Add 'n' to both sides: 5 = n
 Therefore, n = 5

3  1/2n = 0
 Subtract 3 from both sides: 1/2n = 3
 Multiply both sides by 2: n = 6
 Therefore, n = 6

n  4 = 0
 Add 4 to both sides: n = 4
 Therefore, n = 4
Solutions
Therefore, the solutions to the equation (5n)(31/2n)(n4) = 0 are n = 5, n = 6, and n = 4. These are the values of 'n' that make the equation true.