## Solving the Equation: (x+1)(x^2+2x+4)-x^3-3x^2+16=0

This article will guide you through the process of solving the equation (x+1)(x^2+2x+4)-x^3-3x^2+16=0. We will break down each step and explain the reasoning behind it.

### 1. Expanding the Equation

First, we need to expand the left side of the equation. We can do this by multiplying out the brackets:

(x+1)(x^2+2x+4) = x(x^2+2x+4) + 1(x^2+2x+4) = x^3 + 2x^2 + 4x + x^2 + 2x + 4 = x^3 + 3x^2 + 6x + 4

Now our equation looks like this:
**x^3 + 3x^2 + 6x + 4 - x^3 - 3x^2 + 16 = 0**

### 2. Simplifying the Equation

Next, we can simplify the equation by combining like terms:

**6x + 20 = 0**

### 3. Isolating the Variable

To isolate the variable x, we need to subtract 20 from both sides of the equation:

**6x = -20**

### 4. Solving for x

Finally, we can solve for x by dividing both sides of the equation by 6:

**x = -20/6**

### 5. Simplifying the Solution

The solution can be further simplified:

**x = -10/3**

Therefore, the solution to the equation (x+1)(x^2+2x+4)-x^3-3x^2+16=0 is **x = -10/3**.