(x+2)(x+3)-(x-2)(x+5)=6

2 min read Jun 16, 2024

Solving the Equation: (x+2)(x+3)-(x-2)(x+5)=6

This article will guide you through the process of solving the equation (x+2)(x+3)-(x-2)(x+5)=6. We will use algebraic manipulation to isolate the variable 'x' and find its value(s).

Step 1: Expanding the equation

First, we need to expand the equation by multiplying out the brackets:

(x+2)(x+3) = x² + 3x + 2x + 6 = x² + 5x + 6
(x-2)(x+5) = x² + 5x - 2x - 10 = x² + 3x - 10

Now, our equation becomes:

(x² + 5x + 6) - (x² + 3x - 10) = 6

Step 2: Simplifying the equation

Next, we simplify the equation by combining like terms:

x² + 5x + 6 - x² - 3x + 10 = 6
2x + 16 = 6

Step 3: Isolating the variable 'x'

To isolate the 'x' term, we subtract 16 from both sides:

2x + 16 - 16 = 6 - 16
2x = -10

Step 4: Solving for 'x'

Finally, we divide both sides by 2 to solve for 'x':

2x / 2 = -10 / 2
x = -5

Conclusion

Therefore, the solution to the equation (x+2)(x+3)-(x-2)(x+5)=6 is x = -5.