https://file.aiquickdraw.com/mathbot/file/1729798501666ew5z2gyn.jpg

The given equation to solve is:

\[
68w^2 + 90w = 0
\]

### Steps to Solve:

1. **Factor out the common term**:
   Factor out \( w \) from both terms:
   \[
   w(68w + 90) = 0
   \]

2. **Solve for each factor**:
   - \( w = 0 \)
   - For \( 68w + 90 = 0 \):
     \[
     68w = -90
     \]
     \[
     w = \frac{-90}{68} = \frac{-45}{34}
     \]

### Solutions:
Thus, the solutions are:
\[
w = 0, \frac{-45}{34}
\]

Would you like more details on any of the steps or have any questions?

Here are 5 related questions to consider:
1. What are the general steps for solving a quadratic equation by factoring?
2. How do you simplify fractions like \(\frac{-90}{68}\)?
3. What does the zero-product property state in algebra?
4. Can you apply this factorization method to other quadratic equations?
5. What happens if a quadratic equation does not factor easily?

**Tip**: Always check if a common factor can be factored out first when solving equations!

Learn how to solve the quadratic equation 68w^2 + 90w = 0 using factoring. The step-by-step solution covers key algebraic concepts such as factoring and the zero-product property. Suitable for students in Grades 8-10.

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