Solve the quadratic equation 84x2+16x=0 by factoring out the GCF.(1 point) Responses The solutions are x=0 and x=421. The solutions are x equals 0 and x equals Start Fraction 4 over 21 End Fraction . The solutions are x=0 and x=4. The solutions are x equals 0 and x equals 4 . The solutions are x=−421 and x=0. The solutions are x equals negative Start Fraction 4 over 21 End Fraction and x equals 0 . The solutions are x=−4 and x=−421.

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

The GCF of 84 and 16 is 4, so we can factor out 4x:

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

Now, we set each factor equal to zero:

1. \(4x = 0\)
\[ x = 0 \]

2. \(21x + 4 = 0\)
\[ 21x = -4 \]
\[ x = -\frac{4}{21} \]

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

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

Therefore, the correct response is:
The solutions are \( x = 0 \) and \( x = -\frac{4}{21} \).