#### Answer

$t=\left\{ -\dfrac{7}{2},\dfrac{7}{2} \right\}$

#### Work Step by Step

Factoring the given equation, $
4t^2=49
,$ results to
\begin{array}{l}\require{cancel}
4t^2-49=0
\\\\
(2t+7)(2t-7)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(2t+7)(2t-7)=0
,$ are
\begin{array}{l}\require{cancel}
2t+7=0
\\\\
2t=-7
\\\\
t=-\dfrac{7}{2}
,\\\\\text{OR}\\\\
2t-7=0
\\\\
2t=7
\\\\
t=\dfrac{7}{2}
.\end{array}
Hence, $
t=\left\{ -\dfrac{7}{2},\dfrac{7}{2} \right\}
.$