To solve the equation \((2x - 1)(5x + 3) = 0\), we can apply the **zero product property**, which states that if the product of two factors is zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for \(x\):

### Step 1: Set each factor equal to zero
1. \(2x - 1 = 0\)
2. \(5x + 3 = 0\)

### Step 2: Solve each equation
1. **For \(2x - 1 = 0\):**
   \[
   2x = 1 \\
   x = \frac{1}{2}
   \]

2. **For \(5x + 3 = 0\):**
   \[
   5x = -3 \\
   x = -\frac{3}{5}
   \]

### Solution:
The solutions are \(x = \frac{1}{2}\) and \(x = -\frac{3}{5}\).

Would you like more details, or do you have any questions?

Here are five related questions you might find interesting:
1. How would you solve the equation \((3x + 2)(4x - 5) = 0\)?
2. What happens if both factors in the equation have the same solution?
3. How do you solve a quadratic equation that does not factor easily?
4. Can the zero product property be applied to expressions with more than two factors?
5. What is the significance of each solution in the context of graphing the equation?

**Tip:** When solving polynomial equations, always consider checking for common factors first before applying the zero product property.

Learn how to solve the equation (2x - 1)(5x + 3) = 0 with detailed steps. Apply the zero product property to find the solutions and understand the concept of factoring in algebra. Suitable for Grades 7-9.

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