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

This article will guide you through the steps of solving the equation **(x+1)(2x+5) = (2x+3)(x-4) + 5**.

### Expanding the Equation

First, we need to expand both sides of the equation by multiplying out the brackets.

**Left-hand side:**(x+1)(2x+5) = 2x² + 7x + 5**Right-hand side:**(2x+3)(x-4) + 5 = 2x² - 5x - 12 + 5 = 2x² - 5x - 7

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

### Simplifying the Equation

Next, we need to simplify the equation by moving all the terms to one side.

Subtracting 2x² from both sides, we get: **7x + 5 = -5x - 7**

Adding 5x to both sides: **12x + 5 = -7**

Subtracting 5 from both sides: **12x = -12**

### Solving for x

Finally, to isolate x, we divide both sides by 12:

**x = -12 / 12**

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

### Verification

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

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

Since both sides of the equation are equal to 0, our solution x = -1 is correct.