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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**.