## Solving the Quadratic Equation: (x+4)(x-9) = 4x

This article will guide you through solving the quadratic equation (x+4)(x-9) = 4x. We will use algebraic manipulation to arrive at the solution(s) for x.

### Expanding and Simplifying the Equation

First, we need to expand the left side of the equation by multiplying the terms:

(x + 4)(x - 9) = x² - 5x - 36

Now, let's move the 4x term from the right side to the left side by subtracting it from both sides:

x² - 5x - 36 - 4x = 0

Combining like terms, we get the simplified quadratic equation:

x² - 9x - 36 = 0

### Solving the Quadratic Equation

We can solve this equation using a few different methods, including factoring, completing the square, or the quadratic formula. In this case, factoring is the most straightforward method.

**Factoring the Equation**

We need to find two numbers that add up to -9 (the coefficient of the x term) and multiply to -36 (the constant term). These numbers are -12 and 3:

(x - 12)(x + 3) = 0

For the product of two factors to equal zero, one or both of the factors must be equal to zero. Therefore, we have two possible solutions:

x - 12 = 0 or x + 3 = 0

Solving for x in each case:

x = 12 or x = -3

### Conclusion

Therefore, the solutions to the quadratic equation (x+4)(x-9) = 4x are **x = 12** and **x = -3**.