Answer
$t=\dfrac{5}{21}$
Work Step by Step
Using the properties of equality, the value of the variable that satisfies the given equation, $
3(2t-4)+2(3t+1)=-2(4t+3)-(t-1)
,$ is
\begin{array}{l}\require{cancel}
6t-12+6t+2=-8t-6-t+1
\\\\
6t+6t+8t+t=-6+1+12-2
\\\\
21t=5
\\\\
t=\dfrac{5}{21}
.\end{array}
