What are the solutions to the quadratic equation 6x² + 24x = 0?

To solve the quadratic equation 6x² + 24x = 0, we can start by factoring out the common term from both parts of the equation.

We can factor out 6x, which gives us:

6x(x + 4) = 0

Now, we set each factor equal to zero:

1. 6x = 0
2. x + 4 = 0

From the first equation (6x = 0), we divide both sides by 6:

x = 0

From the second equation (x + 4 = 0), we subtract 4 from both sides:

x = -4

The solutions to the quadratic equation 6x² + 24x = 0 are x = 0 and x = -4.