Solve for z. You may enter an exact answer or round to the nearest hundredth. (6x+3)/(3x+1)=(5)/(3) Show your work here

To solve for $x$, we can start by cross-multiplying to get rid of the fractions:<br /><br />$(6x+3) \cdot 3 = 5 \cdot (3x+1)$<br /><br />Expanding both sides, we get:<br /><br />$18x + 9 = 15x + 5$<br /><br />Subtracting $15x$ from both sides, we have:<br /><br />$3x + 9 = 5$<br /><br />Subtracting $9$ from both sides, we get:<br /><br />$3x = -4$<br /><br />Finally, dividing both sides by $3$, we find:<br /><br />$x = -\frac{4}{3}$