To solve the equation:

\[
5(4x - 1)(6x - 5) = 0
\]

We apply the **zero product property**, which states that if the product of multiple factors equals zero, then at least one of the factors must be zero.

### Step 1: Break the equation into factors

Set each factor inside the parentheses equal to zero:

1. \(4x - 1 = 0\)
2. \(6x - 5 = 0\)

### Step 2: Solve for \(x\) in each case

#### Case 1: \(4x - 1 = 0\)

\[
4x = 1 \quad \text{(add 1 to both sides)}
\]
\[
x = \frac{1}{4} \quad \text{(divide by 4)}
\]

#### Case 2: \(6x - 5 = 0\)

\[
6x = 5 \quad \text{(add 5 to both sides)}
\]
\[
x = \frac{5}{6} \quad \text{(divide by 6)}
\]

### Final Answer

The solutions are:

\[
x = \frac{1}{4} \quad \text{or} \quad x = \frac{5}{6}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How does the zero product property apply to more complex equations?
2. What if the equation had three factors instead of two?
3. How do you solve quadratic equations where the product isn’t set to zero?
4. What is the difference between solving linear and quadratic factors?
5. How does factoring help in solving polynomials?

**Tip**: Always simplify each factor separately when using the zero product property.

Learn how to solve the equation 5(4x-1)(6x-5)=0 by applying the zero product property. This solution breaks down the process of factoring and solving for x, making it ideal for students in Grades 8-10 studying algebraic equations.

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