Let's solve the equation step by step:
Starting with the equation:
\[ 7(6x - 2) = -84 \]
First, divide both sides by 7 to simplify the equation:
\[ 6x - 2 = -12 \]
Next, add 2 to both sides to isolate the term with \( x \):
\[ 6x = -12 + 2 \] \[ 6x = -10 \]
Now, divide both sides by 6 to solve for \( x \):
\[ x = \frac{-10}{6} \]
To simplify \( \frac{-10}{6} \):
\[ x = \frac{-5}{3} \]
Thus, the solution \( x = -\frac{5}{3} \) indicates that the equation has:
C: one solution \(-\frac{5}{3}\)