#### Answer

$z=\left\{ -\dfrac{7}{6},\dfrac{7}{6} \right\}$

#### Work Step by Step

Using the properties of equality, the given expression, $
36m^2-9=40
,$ is equivalent to
\begin{array}{l}\require{cancel}
36m^2-9-40=0
\\\\
36m^2-49=0
.\end{array}
Factoring the above equation, $
36m^2-49=0
,$ results to
\begin{array}{l}\require{cancel}
(6m+7)(6m-7)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(6m+7)(6m-7)=0
,$ are
\begin{array}{l}\require{cancel}
6m+7=0
\\\\
6m=-7
\\\\
m=-\dfrac{7}{6}
,\\\\\text{OR}\\\\
6m-7=0
\\\\
6m=7
\\\\
m=\dfrac{7}{6}
.\end{array}
Hence, $
z=\left\{ -\dfrac{7}{6},\dfrac{7}{6} \right\}
.$