Solve the quadratic equation 84x^2+16x=0 by factoring out the GCF.(1 point)

To solve the quadratic equation \( 84x^2 + 16x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms.

The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \).

Now we can factor the equation:

\[
84x^2 + 16x = 4x(21x + 4) = 0
\]

Next, we set each factor equal to zero:

1. \( 4x = 0 \)

This gives us \( x = 0 \).

2. \( 21x + 4 = 0 \)

Solving for \( x \):
\[
21x = -4 \quad \Rightarrow \quad x = -\frac{4}{21}
\]

Thus, the complete solution to the equation is:

\[
x = 0 \quad \text{and} \quad x = -\frac{4}{21}
\]

So, the correct response is:

The solutions are \( x = -\frac{4}{21} \) and \( x = 0 \).