Answer
The solution is $\left\{0, \frac{4}{3}\right\}$.
Work Step by Step
Take the square root of both sides to obtain:
$3z-2 = \pm \sqrt{4}
\\3z-2 = \pm \sqrt{2^2}
\\3z-2 = \pm 2$
Add 2 to both sides to obtain:
$3z = 2 \pm2$
Divide 3 on both sides of the equation to obtain:
$z=\dfrac{2 \pm 2}{3}$
Split the solutions to obtain:
$z_1 = \dfrac{2+2}{3} =\dfrac{4}{3}
\\z_2 = \dfrac{2-2}{3} = 0$
Thus, the solution is $\left\{0, \frac{4}{3}\right\}$.
