Variable $x$ cannot be equal to $\frac{1}{3}$ since division by zero is not defined. Multiply both sides of the equation by $6\left(3x-1\right)$, the least common multiple of $6x-2,3$.
$$3\left(5x+2\right)=4\left(3x-1\right)$$
Use the distributive property to multiply $3$ by $5x+2$.
$$15x+6=4\left(3x-1\right)$$
Use the distributive property to multiply $4$ by $3x-1$.
$$15x+6=12x-4$$
Subtract $12x$ from both sides.
$$15x+6-12x=-4$$
Combine $15x$ and $-12x$ to get $3x$.
$$3x+6=-4$$
Subtract $6$ from both sides.
$$3x=-4-6$$
Subtract $6$ from $-4$ to get $-10$.
$$3x=-10$$
Divide both sides by $3$.
$$x=\frac{-10}{3}$$
Fraction $\frac{-10}{3}$ can be rewritten as $-\frac{10}{3}$ by extracting the negative sign.
