Let's solve the equation step by step:

\[
3(x+2)^2 - 4 = 16
\]

### Step 1: Add 4 to both sides to simplify
\[
3(x+2)^2 = 16 + 4
\]
\[
3(x+2)^2 = 20
\]

### Step 2: Divide both sides by 3
\[
(x+2)^2 = \frac{20}{3}
\]

### Step 3: Take the square root of both sides
\[
x+2 = \pm \sqrt{\frac{20}{3}} = \pm \frac{\sqrt{20}}{\sqrt{3}} = \pm \frac{2\sqrt{5}}{\sqrt{3}}
\]

### Step 4: Rationalize the denominator
\[
x+2 = \pm \frac{2\sqrt{5}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \pm \frac{2\sqrt{15}}{3}
\]

### Step 5: Solve for \( x \)
\[
x = -2 \pm \frac{2\sqrt{15}}{3}
\]

Thus, the two solutions are:
\[
x = -2 + \frac{2\sqrt{15}}{3} \quad \text{or} \quad x = -2 - \frac{2\sqrt{15}}{3}
\]

Would you like more details on any of these steps?

### Related Questions:
1. How do you rationalize a denominator?
2. Can you explain the concept of square roots in equations?
3. What does it mean to "simplify" an equation?
4. How do you handle complex numbers in square root cases?
5. Why do we get two solutions when taking square roots?

**Tip:** When solving quadratic equations, always check if factoring can simplify the process before expanding!

Learn how to solve the quadratic equation 3(x+2)^2 - 4 = 16 with a detailed step-by-step solution. This problem covers algebraic concepts like simplifying equations, solving square roots, and rationalizing denominators. Suitable for students in Grades 9-11.

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