## Solving the Equation (x+2)(x^2-2x+4)-x(x^2-5)=15

This article will guide you through the steps of solving the given equation: **(x+2)(x^2-2x+4)-x(x^2-5)=15**.

### 1. Expanding the Equation

First, we need to expand the equation by multiplying the terms:

**(x+2)(x^2-2x+4)**: This is a special product called the**sum of cubes**. It can be expanded directly as:**x^3 + 2^3 = x^3 + 8****x(x^2-5)**: This simplifies to**x^3 - 5x**

Now our equation looks like this:
**x^3 + 8 - x^3 + 5x = 15**

### 2. Simplifying the Equation

Combining like terms, we get:
**5x + 8 = 15**

### 3. Isolate the Variable

To isolate the variable 'x', we need to subtract 8 from both sides:
**5x = 7**

### 4. Solving for 'x'

Finally, divide both sides by 5 to get the value of x:
**x = 7/5**

Therefore, the solution to the equation **(x+2)(x^2-2x+4)-x(x^2-5)=15** is **x = 7/5**.