FInd the solution s of 6bsquare + 28b=0 Formula: ×=0 and ×=-a over b

To solve the quadratic equation \( 6b^2 + 28b = 0 \), we can follow these steps:

1. **Factor the equation:**

   The equation \( 6b^2 + 28b = 0 \) can be factored by taking out the common factor, which is \( 2b \).

   \[
   2b(3b + 14) = 0
   \]

2. **Set each factor to zero:**

   For the equation to be zero, either \( 2b = 0 \) or \( 3b + 14 = 0 \).

   - **First factor:** \( 2b = 0 \)

     Solving for \( b \):
     \[
     b = 0
     \]

   - **Second factor:** \( 3b + 14 = 0 \)

     Solving for \( b \):
     \[
     3b = -14 \quad \Rightarrow \quad b = -\frac{14}{3}
     \]

3. **Solutions:**

   The solutions for \( b \) are:
   \[
   b = 0 \quad \text{and} \quad b = -\frac{14}{3}
   \]

So, \( b = 0 \) and \( b = -\frac{14}{3} \).

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

Here are 5 related questions:

1. How do you factor a quadratic equation?
2. What is the Quadratic Formula and when is it used?
3. What are the steps to solve a quadratic equation by factoring?
4. Can you have complex solutions in a quadratic equation?
5. How do you determine if a quadratic equation has real or complex solutions?

**Tip:** Always check if you can factor out a common term in a quadratic equation before using more complex methods like the Quadratic Formula!

Learn how to solve the quadratic equation 6b^2 + 28b = 0 using factoring. This step-by-step guide explains key algebraic concepts, including factoring and the zero product property. Suitable for students in Grades 8-10.

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