## Solving the Equation: (5x-1)(x+2)+3(x-4)(x+4)=2(2x+3)^2-8

This article will guide you through the steps of solving the equation:
**(5x-1)(x+2)+3(x-4)(x+4)=2(2x+3)^2-8**

### Expanding the Equation

First, we need to expand all the products in the equation:

**(5x-1)(x+2)**= 5x² + 10x - x - 2 =**5x² + 9x - 2****3(x-4)(x+4)**= 3(x² - 16) =**3x² - 48****2(2x+3)²**= 2(4x² + 12x + 9) =**8x² + 24x + 18**

Now the equation becomes:

**5x² + 9x - 2 + 3x² - 48 = 8x² + 24x + 18 - 8**

### Simplifying the Equation

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

**8x² + 9x - 50 = 8x² + 24x + 10**

Subtracting **8x²** and **10** from both sides:

**9x - 50 = 24x + 10**

Subtracting **9x** and **10** from both sides:

**-60 = 15x**

### Solving for x

Finally, dividing both sides by **15** gives us the solution:

**x = -4**

Therefore, the solution to the equation (5x-1)(x+2)+3(x-4)(x+4)=2(2x+3)^2-8 is **x = -4**.