(2x-3)(2x+3)=4x(x+1)-1

2 min read Jun 16, 2024

Solving the Equation: (2x-3)(2x+3)=4x(x+1)-1

This article will walk you through the steps of solving the equation (2x-3)(2x+3)=4x(x+1)-1. We'll simplify both sides, rearrange terms, and finally solve for the value of 'x'.

1. Expanding the Equation

First, we need to expand both sides of the equation using the distributive property (also known as FOIL for binomials):

Left side: (2x-3)(2x+3) = 4x² - 9 (Using the difference of squares pattern: (a-b)(a+b) = a² - b²)
Right side: 4x(x+1) - 1 = 4x² + 4x - 1

Now, our equation looks like this: 4x² - 9 = 4x² + 4x - 1

2. Simplifying the Equation

Notice that both sides have a 4x² term. Subtracting 4x² from both sides cancels them out, leaving us with:

-9 = 4x - 1

3. Isolating 'x'

Our next step is to isolate the 'x' term. Adding 1 to both sides:

-8 = 4x

4. Solving for 'x'

Finally, we divide both sides by 4 to solve for 'x':

x = -2

Conclusion

Therefore, the solution to the equation (2x-3)(2x+3)=4x(x+1)-1 is x = -2.