#### Answer

$t=\left\{ -\dfrac{3}{5},\dfrac{5}{4} \right\}$

#### Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the Distributive Property, the given expression, $
(2t+1)(4t-1)=14
,$ is equivalent to
\begin{array}{l}\require{cancel}
2t(4t)+2t(-1)+1(4t)+1(-1)=14
\\\\
8t^2-2t+4t-1=14
\\\\
8t^2-2t+4t-1-14=0
\\\\
8t^2+2t-15=0
.\end{array}
Factoring the above equation, $
8t^2+2t-15=0
,$ results to
\begin{array}{l}\require{cancel}
(2t+3)(4t-5)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(2t+3)(4t-5)=0
,$ are
\begin{array}{l}\require{cancel}
2t+3=0
\\\\
2t=-3
\\\\
t=-\dfrac{3}{5}
,\\\\\text{OR}\\\\
4t-5=0
\\\\
4t=5
\\\\
t=\dfrac{5}{4}
.\end{array}
Hence, $
t=\left\{ -\dfrac{3}{5},\dfrac{5}{4} \right\}
.$