Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $3x$, the least common multiple of $x,3$.
$$3\left(3x+2\right)=2x$$
Use the distributive property to multiply $3$ by $3x+2$.
$$9x+6=2x$$
Subtract $2x$ from both sides.
$$9x+6-2x=0$$
Combine $9x$ and $-2x$ to get $7x$.
$$7x+6=0$$
Subtract $6$ from both sides. Anything subtracted from zero gives its negation.
$$7x=-6$$
Divide both sides by $7$.
$$x=\frac{-6}{7}$$
Fraction $\frac{-6}{7}$ can be rewritten as $-\frac{6}{7}$ by extracting the negative sign.
