Solve the quadratic equation 84x2+16x=0

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

The GCF is \(4\). We can factor this out:

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

Next, we continue factoring inside the parentheses:

\[
4x(21x + 4) = 0
\]

Now we have two factors equal to zero:

1. \(4x = 0\)
2. \(21x + 4 = 0\)

For the first factor \(4x = 0\):

\[
x = 0
\]

For the second factor \(21x + 4 = 0\):

\[
21x = -4 \\
x = -\frac{4}{21}
\]

Thus, the solutions to the original equation are:

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

From the provided responses, the correct one is:

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