(3x%2B2)-(4x-11)(2x%2B1)%3D(x-3)(x%2B7).jpeg "(3x-8)(3x+2)-(4x-11)(2x+1)=(x-3)(x+7)")
Solving the Equation: (3x-8)(3x+2)-(4x-11)(2x+1)=(x-3)(x+7)
This article will guide you through solving the equation (3x-8)(3x+2)-(4x-11)(2x+1)=(x-3)(x+7). We'll break down each step to make the process clear and easy to follow.
1. Expanding the Products
First, we need to expand the products on both sides of the equation. This involves using the distributive property (also known as FOIL method):
- Left Side:
- (3x-8)(3x+2) = 9x² + 6x - 24x - 16 = 9x² - 18x - 16
- (4x-11)(2x+1) = 8x² + 4x - 22x - 11 = 8x² - 18x - 11
- Right Side:
- (x-3)(x+7) = x² + 7x - 3x - 21 = x² + 4x - 21
Now our equation looks like this: (9x² - 18x - 16) - (8x² - 18x - 11) = x² + 4x - 21
2. Simplifying the Equation
Next, we simplify the equation by combining like terms:
- 9x² - 8x² - 18x + 18x - 16 + 11 = x² + 4x - 21
- x² - 5 = x² + 4x - 21
3. Isolating the Variable
To isolate the variable (x), we need to move all terms to one side of the equation:
- x² - x² - 4x = -21 + 5
- -4x = -16
4. Solving for x
Finally, we can solve for x by dividing both sides by -4:
- x = -16 / -4
- x = 4
Therefore, the solution to the equation (3x-8)(3x+2)-(4x-11)(2x+1)=(x-3)(x+7) is x = 4.
Conclusion
By following these steps, we successfully solved the given equation. Remember that expanding products, simplifying expressions, and isolating the variable are key techniques used in solving algebraic equations.