solve for m. (-4y-1)(-8y+7)=0 write your answer as integers or as proper or improper fractions in the simplest form

The given equation is:

\[
(-4y - 1)(-8y + 7) = 0
\]

According to the zero product property, if the product of two expressions is zero, then at least one of the expressions must be zero. Thus, we set each factor equal to zero and solve for \( y \).

1. Solve the first factor:
\[
-4y - 1 = 0
\]
Add 1 to both sides:
\[
-4y = 1
\]
Now, divide by \(-4\):
\[
y = \frac{1}{-4} = -\frac{1}{4}
\]

2. Solve the second factor:
\[
-8y + 7 = 0
\]
Subtract 7 from both sides:
\[
-8y = -7
\]
Now, divide by \(-8\):
\[
y = \frac{-7}{-8} = \frac{7}{8}
\]

Thus, the solutions for \( y \) are:

\[
y = -\frac{1}{4} \quad \text{or} \quad y = \frac{7}{8}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve quadratic equations using factoring?
2. Can you explain the zero product property in more depth?
3. What is the difference between proper and improper fractions?
4. How can we graph these solutions on a number line?
5. How would the solution change if it were an inequality instead of an equation?

**Tip:** Always simplify fractions to their lowest terms to ensure your solution is in its simplest form.

Learn how to solve the equation (-4y-1)(-8y+7)=0 by applying the zero product property. This problem involves factoring and solving for y, providing a detailed solution suitable for students in Grades 8-10.

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