4(3x-5)= -2(-x+8)
I got 10x= 4
= 2.5
10x/4 has to equal something though. In this case it is equal to 1 because you've brought the 4 from the RHS onto the LHS by division: $\displaystyle \dfrac{10}{4} x = 1$. From here you'd need to divide both sides by 10/4: $\displaystyle x = \dfrac{1}{\left(\frac{10}{4}\right)}$ and since we divide fractions by "flip n multiply" the RHS is the same as $\displaystyle 1 \times \dfrac{4}{10} = \dfrac{4}{10}$
From the line $\displaystyle 10x = 4$ you can divide both sides by 10 because we want to get x on it's own (which is the same as 1x): $\displaystyle \dfrac{10x}{10} = \dfrac{4}{10}$ and since 10/10 is indeed 1 this is the same as $\displaystyle \dfrac{4}{10}$ which is correct but it's more proper to simplify fractions and so 2/2 was cancelled.
$\displaystyle \dfrac{4}{10} = \dfrac{2 \times 2}{2 \times 5} = \dfrac{2}{5}$.