7*x^*2+13*x*−102=0 how to solve pls explain for beginners im only 6

Sure! Let's take this step by step and keep it super simple.

### Problem:
You have a tricky-looking math problem:
\[ 7x^2 + 13x - 102 = 0 \]

### What does this mean?
This is called a **quadratic equation**. It means we're looking for a number (let's call it **x**) that, when you plug it into this equation, makes the whole thing equal to **0**.

### Steps to Solve:

1. **What does "Factor" mean?**
   - Think of "factoring" like breaking something down into smaller pieces. Imagine you have a LEGO tower, and you want to split it into two smaller towers. In math, factoring means breaking down a complicated expression into simpler expressions that multiply together.

2. **Factor the Equation**:
   - Here, we want to split \(7x^2 + 13x - 102\) into two simpler expressions that look like this:
     \[
     (Ax + B)(Cx + D) = 0
     \]
   - For our equation, it factors like this:
     \[
     (7x + 34)(x - 3) = 0
     \]
     - This is like saying, "If two things multiply to give you zero, one of them must be zero."

3. **Find the Solutions**:
   - Now, set each part equal to zero and solve for **x**:
     - **First part**: \(7x + 34 = 0\)
       - To solve this, you need to make \(x\) by itself:
         \[
         7x = -34 \quad \text{(we moved the 34 to the other side by subtracting it)}
         \]
         \[
         x = -\frac{34}{7} \quad \text{(we divided both sides by 7)}
         \]
     - **Second part**: \(x - 3 = 0\)
       - Here, just move the 3 to the other side:
         \[
         x = 3
         \]

### Final Answer:
So, the two possible solutions are:
1. \( x = -\frac{34}{7} \) (which is a complicated number, but it's still an answer).
2. \( x = 3 \) (which is a nice, simple number).

But remember, sometimes we need to check if these numbers work in the original equation, especially when we deal with logarithms or square roots.

---

**Do you want to ask anything else?**

Here are 5 more questions that might help you:
1. What happens when you multiply two numbers and the result is 0?
2. Can you practice setting simple equations like \(x - 5 = 0\) to solve for \(x\)?
3. How do you divide a number by another number, like when we divided \(-34\) by 7?
4. Why do we move numbers to the other side of the equation when solving for \(x\)?
5. What do you think happens if you get a number like \(x = 3\) that works perfectly in your equation?

**Tip:** When you solve equations, remember that you can always check your answers by plugging them back into the original problem to see if they make the equation true!

Learn how to solve the quadratic equation 7x^2 + 13x - 102 = 0 with a simple step-by-step explanation. This problem involves factoring and applying the Zero Product Property to find the solutions. Suitable for beginners in Grade 1-3.

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