## Solving the Quadratic Equation: 3x(x-4) + 12x - 27 = 0

This article will guide you through the steps of solving the quadratic equation **3x(x-4) + 12x - 27 = 0**.

### 1. Expanding the Equation:

First, we need to simplify the equation by expanding the product:

3x(x-4) + 12x - 27 = 0
3x² - 12x + 12x - 27 = 0
**3x² - 27 = 0**

### 2. Isolating the x² term:

Next, we isolate the x² term by adding 27 to both sides of the equation:

3x² - 27 + 27 = 0 + 27
**3x² = 27**

### 3. Solving for x²:

Now, we solve for x² by dividing both sides by 3:

3x²/3 = 27/3
**x² = 9**

### 4. Taking the Square Root:

To find the value of x, we take the square root of both sides of the equation:

√(x²) = ±√9
**x = ±3**

### 5. Final Solution:

Therefore, the solutions to the quadratic equation **3x(x-4) + 12x - 27 = 0** are **x = 3** and **x = -3**.

### Conclusion

We have successfully solved the quadratic equation by expanding, simplifying, and isolating the x² term. This process demonstrates the importance of applying algebraic techniques to find the roots of polynomial equations.