(x-5)(x+3)=(x-7)(x+4)

Jasonbradley

2 min read Jun 17, 2024

Solving the Equation: (x-5)(x+3) = (x-7)(x+4)

This equation involves expanding brackets and then solving for the unknown variable 'x'. Let's break down the steps:

1. Expand the Brackets

Left-hand side: (x-5)(x+3) = x² - 2x - 15
Right-hand side: (x-7)(x+4) = x² - 3x - 28

Now our equation looks like this: x² - 2x - 15 = x² - 3x - 28

2. Simplify the Equation

Notice that both sides have the term x². Subtracting x² from both sides, we get:

-2x - 15 = -3x - 28

3. Solve for x

Add 3x to both sides: x - 15 = -28
Add 15 to both sides: x = -13

4. Verification

We can verify our answer by plugging x = -13 back into the original equation:

Left-hand side: (-13-5)(-13+3) = (-18)(-10) = 180
Right-hand side: (-13-7)(-13+4) = (-20)(-9) = 180

The left-hand side equals the right-hand side, confirming that x = -13 is the correct solution.

Conclusion

By expanding the brackets, simplifying the equation, and solving for x, we have determined that the solution to the equation (x-5)(x+3) = (x-7)(x+4) is x = -13.