The given equation is:

\[
7(4x - 1)(6x - 5) = 0
\]

To solve this equation, we can use the **zero-product property**, which states that if the product of multiple factors is zero, then at least one of the factors must be zero.

### Step 1: Apply the zero-product property
Since \( 7 \) is a constant and non-zero, we only need to set the two binomials equal to zero:

\[
(4x - 1) = 0 \quad \text{or} \quad (6x - 5) = 0
\]

### Step 2: Solve each equation separately

1. Solve \( 4x - 1 = 0 \):

\[
4x = 1 \quad \Rightarrow \quad x = \frac{1}{4}
\]

2. Solve \( 6x - 5 = 0 \):

\[
6x = 5 \quad \Rightarrow \quad x = \frac{5}{6}
\]

### Final solutions:
The solutions to the equation are:

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

Would you like further details on this process or have any questions?

Here are 5 related questions to explore:

1. How can the zero-product property be applied in other contexts?
2. What happens if one of the factors is a quadratic expression?
3. How do you solve similar equations if they include more complicated factors?
4. Can this technique be extended to equations with more than two factors?
5. What if the equation included fractions or decimals instead of integers?

**Tip:** Always check the factors of an equation carefully to see if any terms are non-zero constants, as they don't affect the solution.

Discover how to solve the algebraic equation 7(4x-1)(6x-5)=0 step by step using the zero-product property. This solution breaks down the application of key concepts, including linear equations and zero-product property, ideal for students in Grades 8-10.

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