## 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**.