Solve Equations with Square Roots: example 9.82

$\begin{array}{cccc}& & & \sqrt{4z-3}=\sqrt{3z+2}\hfill \\ \\ \\ \text{The radical terms are isolated.}\hfill & & & \sqrt{4z-3}=\sqrt{3z+2}\hfill \\ \\ \\ \text{Square both sides of the equation.}\hfill & & & {\left(\sqrt{4z-3}\right)}^2={\left(\sqrt{3z+2}\right)}^2\hfill \\ \\ \\ \text{Simplify, then solve the new equation.}\hfill & & & \begin{array}{c}4z-3=3z+2\hfill \\ z-3=2\hfill \\ z=5\hfill \end{array}\hfill \\ \\ \\ \text{Check the answer.}\hfill & & & \\ \text{We leave it to you to show that 5 checks!}\hfill & & & \text{The solution is}z=5.\hfill \end{array}$