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

This article aims to guide you through the process of solving the equation **(x+1)(2x-3)-3(x-2)=2(x-1)^2**. We will break down each step to ensure a clear understanding of the solution.

### Step 1: Expanding the equation

Begin by expanding the equation, removing the parentheses and simplifying the expression:

**(x+1)(2x-3):**Apply the FOIL method (First, Outer, Inner, Last) to multiply the terms.- (x * 2x) + (x * -3) + (1 * 2x) + (1 * -3) = 2x² - x + 2x - 3 = 2x² + x - 3

**-3(x-2):**Distribute the -3 across the terms inside the parentheses.- -3 * x + (-3) * -2 = -3x + 6

**2(x-1)²:**Square the term (x-1) and then multiply by 2.- 2 * (x-1)² = 2 * (x² - 2x + 1) = 2x² - 4x + 2

Now, the equation becomes:
**2x² + x - 3 - 3x + 6 = 2x² - 4x + 2**

### Step 2: Simplifying the equation

Combine like terms on both sides of the equation to simplify:

**2x² - 2x² + x - 3x + 6 - 3 = -4x + 2****-2x + 3 = -4x + 2**

### Step 3: Isolating the variable

Move all terms containing 'x' to one side of the equation and the constant terms to the other side.

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

### Step 4: Solving for x

Finally, divide both sides by 2 to isolate 'x' and obtain the solution:

**x = -1/2**

### Conclusion

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