(7x+1)(x-3)+20(x-1)(x+1)=3(3x-2)2+13

Jasonbradley

2 min read

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Jun 16, 2024

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Solving the Equation: (7x+1)(x-3)+20(x-1)(x+1)=3(3x-2)2+13

This article will guide you through the steps to solve the equation: (7x+1)(x-3)+20(x-1)(x+1)=3(3x-2)2+13

Expanding the Equation

First, we need to expand the equation by multiplying out the brackets:

• (7x+1)(x-3) = 7x² - 20x - 3
• 20(x-1)(x+1) = 20(x² - 1) = 20x² - 20
• 3(3x-2)² = 3(9x² - 12x + 4) = 27x² - 36x + 12

Now the equation becomes: 7x² - 20x - 3 + 20x² - 20 = 27x² - 36x + 12 + 13

Combining Like Terms

Next, combine the like terms on both sides of the equation:

27x² - 20x - 23 = 27x² - 36x + 25

Solving for x

Now, move all the terms with x to one side of the equation and the constant terms to the other:

16x = 48

Finally, divide both sides by 16 to isolate x:

x = 3

Conclusion

Therefore, the solution to the equation (7x+1)(x-3)+20(x-1)(x+1)=3(3x-2)2+13 is x = 3.