#### Answer

$t=-\dfrac{1}{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|6-5t|=|5t+8|
,$ use the definition of an absolute value equality. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $|x|=|y|$ implies $x=y \text{ or } x=-y,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
6-5t=5t+8
\\\\\text{OR}\\\\
6-5t=-(5t+8)
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
6-5t=5t+8
\\\\
-5t-5t=8-6
\\\\
-10t=2
\\\\
t=\dfrac{2}{-10}
\\\\
t=-\dfrac{1}{5}
\\\\\text{OR}\\\\
6-5t=-(5t+8)
\\\\
6-5t=-5t-8
\\\\
-5t+5t=-8-6
\\\\
0=-14
\text{ (FALSE)}
.\end{array}
Hence, $
t=-\dfrac{1}{5}
.$