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

### Step-by-step solution:

1. Set each factor equal to zero:
   \[
   x + 5 = 0 \quad \text{or} \quad 2x - 3 = 0
   \]

2. Solve each equation separately:

   - For \(x + 5 = 0\):
     \[
     x = -5
     \]

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

### Final solutions:
\[
x = -5 \quad \text{or} \quad x = \frac{3}{2}
\]

Would you like further clarification on any steps?

Here are 5 related questions for further practice:
1. Solve \((x - 4)(3x + 2) = 0\).
2. Solve \( (2x + 1)(x - 7) = 0 \).
3. Solve \( x^2 - 5x + 6 = 0 \) using factoring.
4. Solve \((3x + 2)(x - 6) = 0\).
5. Solve \( (x + 1)(4x - 5) = 0 \).

**Tip:** When solving quadratic equations by factoring, always check if the equation can be factored first before using more complex methods like completing the square or the quadratic formula.

Learn how to solve the quadratic equation (x+5)(2x-3)=0 by applying the zero product property. This problem demonstrates key algebraic techniques such as factoring and is suitable for students in Grades 7-9.

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