## Solving the Equation (x+3)^4 - 13(x+3)^2 + 36 = 0

This equation might look intimidating at first glance, but it can be solved using a simple substitution technique.

### 1. Substitution

Let's introduce a new variable, **y = (x+3)**. This allows us to rewrite the equation as:

**y^4 - 13y^2 + 36 = 0**

This looks much simpler, right? It's now a quadratic equation in terms of y^2.

### 2. Factoring the Quadratic

Now we can factor this equation:

**(y^2 - 9)(y^2 - 4) = 0**

This gives us two possible solutions:

- y^2 - 9 = 0
- y^2 - 4 = 0

### 3. Solving for y

Solving these equations gives us:

- y^2 = 9 => y = ±3
- y^2 = 4 => y = ±2

### 4. Back Substitution

Now we need to substitute back **x + 3** for **y**:

- x + 3 = 3 => x = 0
- x + 3 = -3 => x = -6
- x + 3 = 2 => x = -1
- x + 3 = -2 => x = -5

### 5. Solutions

Therefore, the solutions to the equation (x+3)^4 - 13(x+3)^2 + 36 = 0 are:

**x = 0, x = -6, x = -1, x = -5**