solve the quadratic equation 84x^2+16x=0 by factoring out the GCF

Question

the solution set is x={0,4/21}
the solution set is x={-4/21,0}
the solution set is x={-4, -4/21}
the solution set is x= the solution set is x= {0,4}

Answer 1

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

1. The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \).
2. Factoring out \( 4x \) from the equation gives us:

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

Next, we set each factor equal to zero:

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

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

Therefore, the solution set is:

\[ x = \left{ 0, -\frac{4}{21} \right} \]

So the correct answer from the options you provided is:

The solution set is \( x = \left{ -\frac{4}{21}, 0 \right} \).