solve for m. (-5w+6)(6w-7)=0 write your answer as integers or as proper or improper fractions in the simplest form

The given equation is:

\[
(-5w + 6)(6w - 7) = 0
\]

To solve for \( w \), set each factor equal to zero and solve individually.

### Step 1: Set the first factor equal to zero
\[
-5w + 6 = 0
\]

Solve for \( w \):
\[
-5w = -6
\]
\[
w = \frac{-6}{-5} = \frac{6}{5}
\]

### Step 2: Set the second factor equal to zero
\[
6w - 7 = 0
\]

Solve for \( w \):
\[
6w = 7
\]
\[
w = \frac{7}{6}
\]

### Final Answer:
The solutions for \( w \) are:

\[
w = \frac{6}{5} \quad \text{or} \quad w = \frac{7}{6}
\]

Let me know if you'd like further details or clarifications!

### Related Questions:
1. How do you factor quadratic equations?
2. What are common methods for solving polynomial equations?
3. Can you explain the zero product property in more detail?
4. How do you simplify improper fractions?
5. What are the steps to solve multi-variable linear equations?

**Tip:** When solving equations, always check for extraneous solutions, especially if square roots or fractions are involved.

Learn how to solve the factored equation (-5w + 6)(6w - 7) = 0 using the zero product property. This detailed step-by-step solution explains how to find the values of w and simplifies the answer into fractions. Ideal for students in Grades 8-10.

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