(x-7)(x+3)=x(x+2)+5

2 min read Jun 17, 2024

Solving the Equation: (x-7)(x+3) = x(x+2) + 5

This article will guide you through the process of solving the equation (x-7)(x+3) = x(x+2) + 5. We'll break down each step to ensure a clear understanding.

1. Expand Both Sides of the Equation

First, we need to expand both sides of the equation to get rid of the parentheses:

Left Side: (x-7)(x+3) = x² - 4x - 21
Right Side: x(x+2) + 5 = x² + 2x + 5

Now, the equation becomes: x² - 4x - 21 = x² + 2x + 5

2. Simplify the Equation

We can simplify the equation by subtracting x² from both sides, resulting in:

-4x - 21 = 2x + 5

3. Isolate the Variable

To isolate the variable 'x', we need to move all the 'x' terms to one side and the constant terms to the other side. We can do this by:

Adding 4x to both sides: -21 = 6x + 5
Subtracting 5 from both sides: -26 = 6x

4. Solve for 'x'

Finally, we can solve for 'x' by dividing both sides by 6:

x = -26/6

x = -13/3

Conclusion

Therefore, the solution to the equation (x-7)(x+3) = x(x+2) + 5 is x = -13/3.