Answer
$t=-\dfrac{11}{4}$
Work Step by Step
Using the properties of equality, the value of the variable that satisfies the given equation, $
-(t-3)-(2t+1)=3(t+5)-2(t+1)
,$ is
\begin{array}{l}\require{cancel}
-t+3-2t-1=3t+15-2t-2
\\\\
-t-2t-3t+2t=15-2-3+1
\\\\
-4t=11
\\\\
t=\dfrac{11}{-4}
\\\\
t=-\dfrac{11}{4}
.\end{array}
