Solve for all values of x*x* by factoring.

x, squared, minus, 8, x, minus, 6, equals, minus, 6

*x*2−8*x*−6=

−6

We are given the equation:

\[
x^2 - 8x - 6 = -6
\]

### Step 1: Simplify the equation
Start by adding 6 to both sides to eliminate the \(-6\) from the right-hand side:

\[
x^2 - 8x - 6 + 6 = -6 + 6
\]

This simplifies to:

\[
x^2 - 8x = 0
\]

### Step 2: Factor the equation
Now, we factor the left-hand side. The common factor in both terms is \(x\), so we factor \(x\) out:

\[
x(x - 8) = 0
\]

### Step 3: Solve for \(x\)
To solve for \(x\), set each factor equal to zero:

1. \(x = 0\)
2. \(x - 8 = 0 \Rightarrow x = 8\)

### Solution:
The solutions are:
\[
x = 0 \quad \text{or} \quad x = 8
\]

Would you like more details or explanations? 

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Here are 5 related questions to consider:
1. How would you solve if the quadratic equation was \(x^2 - 8x + 6 = 0\)?
2. How do you use the quadratic formula for solving non-factorable quadratics?
3. What is the significance of factoring in solving polynomial equations?
4. How do you complete the square for an equation like \(x^2 - 8x = 0\)?
5. How can you solve \(x^2 - 8x = 10\)?

**Tip:** Always check if you can factor a quadratic equation before applying more complex methods!

Solve for all values of x by factoring: x^2 - 8x - 6 = -6

Learn how to solve the quadratic equation x^2 - 8x - 6 = -6 by factoring. This step-by-step guide covers essential algebraic techniques and concepts like the zero product property, factoring, and simplifying quadratic equations. Suitable for students in Grades 8-10.

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