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

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

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

Let's break down the steps to find the solution:

### 1. Expanding the Equation

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

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

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

Now, our equation becomes:

**x^3 + 3x^2 + x - 1 - x^3 - 3x^2 = 4**

### 2. Simplifying the Equation

Notice that the x^3 and 3x^2 terms cancel out:

**x - 1 = 4**

### 3. Solving for x

Finally, we isolate x:

- x = 4 + 1
**x = 5**

Therefore, the solution to the equation (x+1)(x^2+2x-1)-x^2(x+3)=4 is **x = 5**.