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

This article will guide you through the process of solving the polynomial equation:

**(x^2-4x+16)(x+4)-x(x+1)(x+2)+3x^2=0**

### Step 1: Expand the Equation

First, we need to expand the equation by multiplying out the brackets:

**(x^2-4x+16)(x+4):**- x^3 - 4x^2 + 16x + 4x^2 - 16x + 64 = x^3 + 64

**-x(x+1)(x+2):**- -x(x^2 + 3x + 2) = -x^3 - 3x^2 - 2x

Now, our equation becomes:

**x^3 + 64 - x^3 - 3x^2 - 2x + 3x^2 = 0**

### Step 2: Simplify the Equation

We can simplify the equation by combining like terms:

**-2x + 64 = 0**

### Step 3: Solve for x

Now, we can solve for x by isolating it:

**-2x = -64****x = -64 / -2****x = 32**

### Solution

Therefore, the solution to the polynomial equation (x^2-4x+16)(x+4)-x(x+1)(x+2)+3x^2=0 is **x = 32**.