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

This article will guide you through the process of solving the equation (x+4)(x-1) = -x^2 + 3x + 4.

### Step 1: Expanding the Left Side

The left side of the equation is a product of two binomials. We can expand it using the FOIL method (First, Outer, Inner, Last).

**First:**(x) * (x) = x^2**Outer:**(x) * (-1) = -x**Inner:**(4) * (x) = 4x**Last:**(4) * (-1) = -4

Combining these terms, we get:
(x+4)(x-1) = x^2 - x + 4x - 4 = **x^2 + 3x - 4**

### Step 2: Rewriting the Equation

Now our equation becomes:
**x^2 + 3x - 4 = -x^2 + 3x + 4**

### Step 3: Bringing All Terms to One Side

To solve for x, we need to bring all terms to one side of the equation. We can do this by adding x^2, subtracting 3x, and subtracting 4 from both sides.

**2x^2 - 8 = 0**

### Step 4: Solving for x

The resulting equation is a quadratic equation. We can solve it by factoring or using the quadratic formula.

**Factoring:**

- 2x^2 - 8 = 0
- 2(x^2 - 4) = 0
- 2(x+2)(x-2) = 0
- Therefore, x = -2 or x = 2

**Quadratic Formula:**

- For the equation ax^2 + bx + c = 0, the quadratic formula is: x = (-b ± √(b^2 - 4ac)) / 2a
- In our equation, a = 2, b = 0, and c = -8. Substituting these values into the quadratic formula, we get: x = (0 ± √(0^2 - 4 * 2 * -8)) / (2 * 2)
- x = (± √64) / 4
- x = (± 8) / 4
- Therefore, x = 2 or x = -2

### Conclusion

Therefore, the solutions to the equation (x+4)(x-1) = -x^2 + 3x + 4 are **x = 2** and **x = -2**.