(x-3)(x+4)-(x-5)(x+2)=6

2 min read Jun 17, 2024

Solving the Equation: (x-3)(x+4)-(x-5)(x+2)=6

This article will guide you through the process of solving the equation (x-3)(x+4)-(x-5)(x+2)=6. We will break down the steps and explain the reasoning behind each action.

Expanding the Equation

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

(x-3)(x+4): Using the FOIL method (First, Outer, Inner, Last), we get:
- x² + 4x - 3x - 12 = x² + x - 12
(x-5)(x+2): Similarly, we get:
- x² + 2x - 5x - 10 = x² - 3x - 10

Now, the equation becomes: x² + x - 12 - (x² - 3x - 10) = 6

Simplifying the Equation

We can now simplify the equation by removing the brackets and combining like terms:

x² + x - 12 - x² + 3x + 10 = 6
4x - 2 = 6

Isolating the Variable

To isolate the variable x, we will first add 2 to both sides of the equation:

4x = 8

Solving for x

Finally, we divide both sides of the equation by 4 to find the value of x:

x = 2

Conclusion

Therefore, the solution to the equation (x-3)(x+4)-(x-5)(x+2)=6 is x = 2.

Remember that you can always check your answer by substituting the value of x back into the original equation. In this case, if you substitute x = 2 into the original equation, both sides of the equation should be equal to 6, confirming that our solution is correct.