Solve the equation using the Zero-Product Property.

To solve this equation using the Zero-Product Property, we need to set each factor (–2x and (5x – 2)) equal to 0 and solve for x.

Setting –2x = 0:
-2x = 0
x = 0

Setting (5x – 2) = 0:
5x - 2 = 0
5x = 2
x = 2/5

Therefore, the solutions to the equation –2x(5x – 2) = 0 are x = 0 and x = 2/5, which is equivalent to x = 0 and x = 2 over 5.

So, the correct answer is:

a. x = 0, 2 over 5