Question

To solve the quadratic equation \( 84x^2 + 16x = 0 \), we can factor out the common term:

\[
x(84x + 16) = 0
\]

Setting each factor to zero gives us:

1. \( x = 0 \)
2. \( 84x + 16 = 0 \)

Now, solving for \( x \) in the second equation:

\[
84x + 16 = 0 \\
84x = -16 \\
x = \frac{-16}{84} \\
x = \frac{-2}{10.5} \\
x = \frac{-2}{\frac{21}{2}} \\
x = \frac{-4}{21}
\]

Thus, the solutions to the equation are:

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

The correct answer that resembles this solution is \( x=0 \) and \( x=-421 \), given that the last solution simplifies to that in context is incorrect.

None of the provided responses match the correct solutions. Therefore, the quadratic equation has answers \( x=0 \) and \( x = -\frac{4}{21} \). Please check the options provided or clarify further.