Solve the quadratic equation 84x^2+16x=0

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

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

Setting each factor equal to zero gives us two possible solutions:

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

Now, solving the second equation:

\[
84x + 16 = 0 \implies 84x = -16 \implies x = -\frac{16}{84}
\]

Simplifying \(-\frac{16}{84}\):

\[
-\frac{16}{84} = -\frac{4}{21}
\]

Thus, the solutions to the equation \(84x^2 + 16x = 0\) are:

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

So the correct response is:

**x = −4/21 and x = 0**.