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

This article will guide you through the process of solving the given equation: **(x+1)(2x-3) = (2x-1)(x+5)**. We will use algebraic manipulation to isolate the variable 'x' and find its solution.

### Expanding the Equation

The first step is to expand both sides of the equation by multiplying the expressions within the parentheses:

**Left side:**(x+1)(2x-3) = 2x² - x - 3**Right side:**(2x-1)(x+5) = 2x² + 9x - 5

Now our equation looks like this:
**2x² - x - 3 = 2x² + 9x - 5**

### Simplifying the Equation

Notice that the term 2x² appears on both sides of the equation. We can subtract 2x² from both sides to eliminate it:

**-x - 3 = 9x - 5**

### Isolating the Variable 'x'

Next, we want to isolate 'x' on one side of the equation. Let's move all terms containing 'x' to the left side and the constant terms to the right side:

-x - 9x = -5 + 3

This simplifies to:
**-10x = -2**

### Solving for 'x'

Finally, we divide both sides of the equation by -10 to find the value of 'x':

**x = -2 / -10**

**x = 1/5**

### Conclusion

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