https://file.aiquickdraw.com/mathbot/file/1726781909176qs18akgz.jpg

The equation provided in the image is:

\[
(x - 2)(x - 4) = 8
\]

To solve this, follow these steps:

### Step 1: Expand the left-hand side
First, expand the product of \((x - 2)(x - 4)\):

\[
(x - 2)(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\]

### Step 2: Set the equation equal to zero
The original equation is:

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

Subtract 8 from both sides:

\[
x^2 - 6x + 8 - 8 = 0 \implies x^2 - 6x = 0
\]

### Step 3: Factor the quadratic equation
Factor \(x^2 - 6x = 0\):

\[
x(x - 6) = 0
\]

### Step 4: Solve for \(x\)
The solutions to this equation are:

\[
x = 0 \quad \text{or} \quad x - 6 = 0 \implies x = 6
\]

### Final Answer:
The solutions to the equation are:

\[
x = 0 \quad \text{and} \quad x = 6
\]

Would you like further details or explanations?

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Here are 5 related questions you might find helpful:
1. How do you solve quadratic equations using the factoring method?
2. What is the process of expanding binomials?
3. How can we use the quadratic formula for solving similar problems?
4. What other methods can we use to solve quadratic equations besides factoring?
5. Can you explain how to complete the square for solving quadratic equations?

**Tip:** Always double-check your algebraic manipulations by plugging your solutions back into the original equation!

What are the solutions to the equation (x - 2)(x - 4) = 8?

Learn how to solve the quadratic equation (x - 2)(x - 4) = 8 step-by-step. This problem covers key algebraic concepts such as factoring, solving quadratic equations, and the Zero Product Property. Suitable for students in Grades 8-10.

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