Answer
$t=\left\{ -\dfrac{5}{3},\dfrac{5}{3} \right\}$
Work Step by Step
Factoring the given equation, $
9t^2=25
,$ results to
\begin{array}{l}\require{cancel}
9t^2-25=0
\\\\
(3t+5)(3t-5)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(3t+5)(3t-5)=0
,$ are
\begin{array}{l}\require{cancel}
3t+5=0
\\\\
3t=-5
\\\\
t=-\dfrac{5}{3}
,\\\\\text{OR}\\\\
3t-5=0
\\\\
3t=5
\\\\
t=\dfrac{5}{3}
.\end{array}
Hence, $
t=\left\{ -\dfrac{5}{3},\dfrac{5}{3} \right\}
.$
