To solve the equation \(12x + 48 = h(2x + 8)\), let's follow these steps:

### Step 1: Factor the Left Side
We can factor the left side of the equation:
\[
12x + 48 = 12(x + 4)
\]
So, the equation becomes:
\[
12(x + 4) = h(2x + 8)
\]

### Step 2: Compare Coefficients
Since the equation must hold true for all values of \(x\), the expressions inside the parentheses must be equal, and the coefficients of the factored terms must also be equal. Thus, we have:
\[
12 = h
\]
and
\[
x + 4 = 2x + 8
\]

### Step 3: Solve for \(x\)
Let's solve the equation \(x + 4 = 2x + 8\):
\[
x + 4 = 2x + 8
\]
Subtract \(x\) from both sides:
\[
4 = x + 8
\]
Subtract 8 from both sides:
\[
x = -4
\]

### Final Answer:
- The value of \(h\) is \(12\).
- The value of \(x\) is \(-4\).

Do you want more details or have any questions?

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Here are five related questions you might find helpful:
1. What happens if we change the equation to \(15x + 45 = h(3x + 9)\)?
2. How do we solve equations with variables on both sides without factoring?
3. What are some examples of linear equations in one variable?
4. Can you explain the concept of like terms and how they are combined?
5. What are the steps to check the solution to an equation?

**Tip:** When solving linear equations, always try to simplify both sides of the equation as much as possible before solving for the variable.

Learn how to solve the equation 12x + 48 = h(2x + 8) with a detailed step-by-step solution. This problem covers equations, factoring, coefficient comparison, and solving linear equations. Suitable for students in Grades 9-12.

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