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Let's go through part (c) and solve the equation step by step. The given equation is:

\[
(x + 4)(x - 6) = 6
\]

### Step 1: Expand the left-hand side

First, expand the product:

\[
(x + 4)(x - 6) = x^2 - 6x + 4x - 24
\]

Simplify:

\[
x^2 - 2x - 24 = 6
\]

### Step 2: Rearrange the equation

Now, move all terms to one side of the equation:

\[
x^2 - 2x - 24 - 6 = 0
\]

Simplify:

\[
x^2 - 2x - 30 = 0
\]

### Step 3: Solve the quadratic equation

You can solve the quadratic equation \(x^2 - 2x - 30 = 0\) using the quadratic formula. The quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \(x^2 - 2x - 30 = 0\), the coefficients are:
- \(a = 1\)
- \(b = -2\)
- \(c = -30\)

Substitute these values into the quadratic formula:

\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-30)}}{2(1)}
\]

\[
x = \frac{2 \pm \sqrt{4 + 120}}{2}
\]

\[
x = \frac{2 \pm \sqrt{124}}{2}
\]

\[
x = \frac{2 \pm 11.1355}{2}
\]

### Step 4: Calculate the two possible values of \(x\)

Now, calculate the two possible values of \(x\):

\[
x_1 = \frac{2 + 11.1355}{2} = \frac{13.1355}{2} = 6.56775
\]

\[
x_2 = \frac{2 - 11.1355}{2} = \frac{-9.1355}{2} = -4.56775
\]

### Final Answer:
The two possible values of \(x\) to 3 decimal places are:
- \(x_1 = 6.568\)
- \(x_2 = -4.568\)

Let me know if you would like more details on any step! 

Here are 5 related questions to expand on this:
1. What is the significance of the quadratic formula in solving quadratic equations?
2. How do you know when to use the quadratic formula instead of factoring?
3. Can every quadratic equation be solved using factoring, or are there cases where it can't be done?
4. Why do we get two possible solutions for a quadratic equation?
5. How would the solutions change if the equation was \( (x + 4)(x - 6) = 12 \) instead of 6?

**Tip:** Always check the discriminant \(b^2 - 4ac\) before solving a quadratic equation—it can tell you if the solutions are real or complex.

Please solve part c of the equation where (x + 4)(x - 6) = 6, and find the two possible values of x.

This step-by-step guide demonstrates how to solve the quadratic equation (x + 4)(x - 6) = 6. Key topics include expanding binomials and applying the quadratic formula to find the two possible values of x. Ideal for students in Grades 9-10.

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