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

This equation involves expanding brackets and simplifying to solve for the unknown variable 'x'. Let's break it down step-by-step:

**1. Expanding the brackets**

- On the left side: (x+1)(2x+5) = 2x² + 5x + 2x + 5 = 2x² + 7x + 5
- On the right side: (2x+3)(x-4) + 5 = 2x² - 8x + 3x - 12 + 5 = 2x² - 5x - 7

**2. Simplifying the equation**

Now the equation becomes: 2x² + 7x + 5 = 2x² - 5x - 7

**3. Isolating the 'x' term**

- Subtract 2x² from both sides: 7x + 5 = -5x - 7
- Add 5x to both sides: 12x + 5 = -7
- Subtract 5 from both sides: 12x = -12

**4. Solving for 'x'**

- Divide both sides by 12: x = -1

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

**Verification:**

To verify the solution, we can substitute x = -1 back into the original equation:

- Left side: (-1+1)(2(-1)+5) = 0 * 3 = 0
- Right side: (2(-1)+3)(-1-4)+5 = 1 * (-5) + 5 = 0

As both sides equal 0, our solution x = -1 is correct.