## Solving the Equation: (5x-1)(x+1)-2(x-3)^2=(x+2)(3x-1)-(x+4)^2+(x^2-x)

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

**(5x-1)(x+1)-2(x-3)^2=(x+2)(3x-1)-(x+4)^2+(x^2-x)**

### Step 1: Expanding the Equation

Start by expanding all the products and squares in the equation:

**(5x-1)(x+1) = 5x² + 4x - 1****-2(x-3)² = -2(x² - 6x + 9) = -2x² + 12x - 18****(x+2)(3x-1) = 3x² + 5x - 2****-(x+4)² = -(x² + 8x + 16) = -x² - 8x - 16**

Now, substitute these expanded expressions back into the original equation:

**5x² + 4x - 1 - 2x² + 12x - 18 = 3x² + 5x - 2 - x² - 8x - 16 + x² - x**

### Step 2: Combining Like Terms

Next, combine the terms on both sides of the equation:

**3x² + 16x - 19 = 3x² - 4x - 26**

### Step 3: Isolating the Variable

To solve for *x*, bring all the *x* terms to one side and the constant terms to the other:

**16x + 4x = -26 + 19**

**20x = -7**

### Step 4: Solving for x

Finally, divide both sides by 20 to isolate *x*:

**x = -7/20**

### Conclusion

Therefore, the solution to the equation (5x-1)(x+1)-2(x-3)²=(x+2)(3x-1)-(x+4)²+(x²-x) is **x = -7/20**.