Use the zero product property to solve the equation:

-3n(2n-5)=0

if ab=0, then a=0 or b=0, so

n=0 or 2n-5=0

n=0 or 5/2

To solve the equation -3n(2n-5) = 0 using the zero product property, we need to set each factor equal to zero and solve for n.

Step 1: Set the first factor -3n equal to zero:
-3n = 0

Step 2: Solve for n by dividing both sides of the equation by -3:
n = 0 / -3
n = 0

Step 3: Set the second factor 2n-5 equal to zero:
2n-5 = 0

Step 4: Solve for n by adding 5 to both sides of the equation:
2n = 5
n = 5 / 2
n = 2.5

Therefore, the solutions to the equation -3n(2n-5) = 0 are n = 0 and n = 2.5.