Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $2x$, the least common multiple of $x,2$.
$$2\times \frac{-4}{9}=x\left(-3\right)$$
Fraction $\frac{-4}{9}$ can be rewritten as $-\frac{4}{9}$ by extracting the negative sign.
$$2\left(-\frac{4}{9}\right)=x\left(-3\right)$$
Express $2\left(-\frac{4}{9}\right)$ as a single fraction.
$$\frac{2\left(-4\right)}{9}=x\left(-3\right)$$
Multiply $2$ and $-4$ to get $-8$.
$$\frac{-8}{9}=x\left(-3\right)$$
Fraction $\frac{-8}{9}$ can be rewritten as $-\frac{8}{9}$ by extracting the negative sign.
$$-\frac{8}{9}=x\left(-3\right)$$
Swap sides so that all variable terms are on the left hand side.
$$x\left(-3\right)=-\frac{8}{9}$$
Divide both sides by $-3$.
$$x=\frac{-\frac{8}{9}}{-3}$$
Express $\frac{-\frac{8}{9}}{-3}$ as a single fraction.
$$x=\frac{-8}{9\left(-3\right)}$$
Multiply $9$ and $-3$ to get $-27$.
$$x=\frac{-8}{-27}$$
Fraction $\frac{-8}{-27}$ can be simplified to $\frac{8}{27}$ by removing the negative sign from both the numerator and the denominator.
