(3x-2)(x+4)-3(x+5)(x-1)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (3x-2)(x+4) - 3(x+5)(x-1) = 0

This equation is a quadratic equation in disguise. Let's break it down and solve for the value of 'x'.

1. Expanding the Equation

First, we need to expand the products on both sides of the equation:

• (3x-2)(x+4) = 3x² + 10x - 8
• (x+5)(x-1) = x² + 4x - 5

Substituting these expanded forms back into the original equation:

3x² + 10x - 8 - 3(x² + 4x - 5) = 0

2. Simplifying the Equation

Now, distribute the -3:

3x² + 10x - 8 - 3x² - 12x + 15 = 0

Combine like terms:

-2x + 7 = 0

3. Solving for x

Isolate the 'x' term:

-2x = -7

Finally, divide both sides by -2:

x = -7 / -2 = 3.5

Conclusion

Therefore, the solution to the equation (3x-2)(x+4) - 3(x+5)(x-1) = 0 is x = 3.5.