Answer
$2y^{2}+3y+5$
Work Step by Step
$\begin{array}{ccccccccccc}
& & 2y^{2} & +3y & +5 & \\
& &--&-- &--& \\
3y-1&) & 6y^{3} &+7y^{2} & +12y& -5 & & \\
& & 6y^{3} & -2y^{2} & & & \color{red}{\leftarrow \small{2y^{2}(3y-1) } } \\
& &--&-- & & & \color{red}{ \small{subtract}} \\
& & & 9y^{2} & +12y& -5 & \\
& & & 9y^{2} & -3y& & \color{red}{\leftarrow \small{3y(3y-1) } }\\
& & &--&-- & &\color{red}{ \small{subtract}} \\
& & & & 15y & -5 & \\
& & & & 15y & -5 & \color{red}{\leftarrow \small{5(3y-1) } }\\
& & & &-- & -- &\color{red}{ \small{subtract}} \\
& & & & & 0 &
\end{array}$
Quotient = $2y^{2}+3y+5$
Remainder = $ 0$.
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{ 6y^{3}+7y^{2}+12y-5}{3y-1}$ = $2y^{2}+3y+5$
