"Find the solution of the following equations: (7x + 3) (5x - 1) = 0"

To solve the given equation:

\[
(7x + 3)(5x - 1) = 0
\]

We use the **zero product property**, which states that if \( a \times b = 0 \), then either \( a = 0 \) or \( b = 0 \).

So, we can split the equation into two simpler equations:

1. \( 7x + 3 = 0 \)
2. \( 5x - 1 = 0 \)

### Solving the first equation:

\[
7x + 3 = 0
\]
Subtract 3 from both sides:

\[
7x = -3
\]
Now, divide by 7:

\[
x = \frac{-3}{7}
\]

### Solving the second equation:

\[
5x - 1 = 0
\]
Add 1 to both sides:

\[
5x = 1
\]
Now, divide by 5:

\[
x = \frac{1}{5}
\]

### Final solutions:
The solutions are:

\[
x = \frac{-3}{7} \quad \text{or} \quad x = \frac{1}{5}
\]

Do you need any further details or have any questions?

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Here are 5 related questions for further exploration:

1. What is the **zero product property** in detail?
2. How would you solve a quadratic equation that doesn't factor neatly?
3. Can you explain how to check if these solutions are correct?
4. What if the product of two binomials was **not** equal to zero?
5. How would this problem change if one binomial were squared?

**Tip**: Always verify solutions by substituting them back into the original equation!

Find the solution of the following equations: (7x + 3) (5x - 1) = 0

Discover how to solve the equation (7x + 3)(5x - 1) = 0 using the zero product property. This step-by-step solution breaks down the process of solving linear equations and is perfect for students in Grades 7-9.

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