To solve the quadratic equation \(5x^2 + 75x = 0\) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms.
The GCF of \(5x^2\) and \(75x\) is \(5x\). Now, we can factor out \(5x\) from the equation:
\[
5x(x + 15) = 0
\]
Next, we set each factor equal to zero:
1. \(5x = 0\) which gives \(x = 0\)
2. \(x + 15 = 0\) which gives \(x = -15\)
Therefore, the solutions to the equation are:
\[
x = 0 \quad \text{and} \quad x = -15
\]
Thus, the correct response is:
**The solutions are \(x = -15\) and \(x = 0\).**