The root of polynomial $ p(t) $ is:
$$ \begin{aligned}t &= -\dfrac{ 1 }{ 9 } \end{aligned} $$Step 1:
Combine like terms:
$$ \color{blue}{10t} + \, \color{red}{ \cancel{5t}} \, \, \color{orange}{ -\cancel{5t}} \,+1 \color{orange}{-t} = \color{orange}{9t} +1 $$Step 2:
$$ \begin{aligned} 9t+1 & = 0 \\[1 em] 9 \cdot t & = -1 \\[1 em] t & = - \frac{ 1 }{ 9 } \end{aligned} $$