#### Answer

$t=\left\{ -6,0 \right\}$

#### Work Step by Step

Factoring the given equation, $
6t+t^2=0
,$ results to
\begin{array}{l}\require{cancel}
t(6+t)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
t(6+t)=0
,$ are
\begin{array}{l}\require{cancel}
t=0
,\\\\\text{OR}\\\\
6+t=0
\\\\
t=-6
.\end{array}
Hence, $
t=\left\{ -6,0 \right\}
.$