Solve the quadratic equation 84x2+16x=0 by factoring out the GCF.

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

The GCF of \( 84 \) and \( 16 \) is \( 4 \). Therefore, we can factor out \( 4x \) (since \( x \) is also a common factor):

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

Now we have the equation factored as:

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

To find the solutions, we can set each factor equal to zero:

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

For the first equation, \( 4x = 0 \):

\[
x = 0
\]

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

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

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

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