## Solving the Equation: (6x-3)(2x+4)+(4x-1)(5-3x) = -21

This article will guide you through the steps to solve the equation: **(6x-3)(2x+4)+(4x-1)(5-3x) = -21**.

### Step 1: Expand the Products

First, we need to expand the products on the left-hand side of the equation using the distributive property (or FOIL method).

**(6x-3)(2x+4)**= 12x² + 24x - 6x - 12 = 12x² + 18x - 12**(4x-1)(5-3x)**= 20x - 12x² - 5 + 3x = -12x² + 23x - 5

Now our equation becomes: **12x² + 18x - 12 - 12x² + 23x - 5 = -21**

### Step 2: Simplify the Equation

Next, combine the like terms on the left-hand side of the equation:

**41x - 17 = -21**

### Step 3: Isolate the Variable

To isolate the variable (x), add 17 to both sides of the equation:

**41x = -4**

### Step 4: Solve for x

Finally, divide both sides of the equation by 41 to get the value of x:

**x = -4/41**

### Conclusion

Therefore, the solution to the equation **(6x-3)(2x+4)+(4x-1)(5-3x) = -21** is **x = -4/41**.