Solve the quadratic equation 5x^2 + 75x = 0 by factoring out the GCF.

To solve the quadratic equation \( 5x^2 + 75x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF in the expression.

The GCF of \( 5x^2 \) and \( 75x \) is \( 5x \). We can factor this out:

\[ 5x(x + 15) = 0 \]

Now, we can set each factor equal to zero:

1. \( 5x = 0 \)
2. \( x + 15 = 0 \)

For the first equation \( 5x = 0 \):

\[ x = 0 \]

For the second equation \( x + 15 = 0 \):

\[ x = -15 \]

Thus, the solutions to the equation \( 5x^2 + 75x = 0 \) are \( x = 0 \) and \( x = -15 \).

Therefore, the correct answer is:

D. The solutions are x = -15 and x = 0.