To solve the equation \( 5x(2x - 3) = 0 \), we can use the property that if the product of two factors is zero, at least one of the factors must be zero.

We can split this equation into two parts:

1. \( 5x = 0 \)
2. \( 2x - 3 = 0 \)

**Solving the first equation:**
\[
5x = 0
\]
Dividing both sides by 5:
\[
x = 0
\]

**Solving the second equation:**
\[
2x - 3 = 0
\]
Adding 3 to both sides:
\[
2x = 3
\]
Dividing both sides by 2:
\[
x = \frac{3}{2}
\]

**Final solutions:**
The solutions to the equation \( 5x(2x - 3) = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = \frac{3}{2}
\]