Which gives all the solutions of left-parenthesis 21 x squared plus 14 x right-parenthesis equals 0?

Question

Answer options with 5 options
A.
negative 2-thirds only

B.
0 and negative 2-thirds

C.
0 only

D.
2-thirds only

E.
0 and 2-thirds

Answer 1

To solve the equation \( 21x^2 + 14x = 0 \), we can factor out the common term:

\[ 7x(3x + 2) = 0 \]

Setting each factor equal to zero gives us:

1. \( 7x = 0 \) which simplifies to \( x = 0 \)
2. \( 3x + 2 = 0 \) which simplifies to \( 3x = -2 \) or \( x = -\frac{2}{3} \)

Thus, the solutions to the equation are \( x = 0 \) and \( x = -\frac{2}{3} \).

Looking at the provided answer options, the correct choice is:

B. \( 0 \) and \( -\frac{2}{3} \).