$$ \begin{aligned} k+3-5k &= -2(k-(4k+1))&& \text{simplify left and right hand side} \\[1 em]-4k+3 &= -2(1k-4k-1)&& \\[1 em]-4k+3 &= -2(-3k-1)&& \\[1 em]-4k+3 &= -(-6k-2)&& \\[1 em]-4k+3 &= 6k+2&& \text{move the $ \color{blue}{ 6k } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]-4k-6k &= 2-3&& \text{simplify left and right hand side} \\[1 em]-10k &= -1&& \text{ divide both sides by $ -10 $ } \\[1 em]k &= \frac{-1}{-10}&& \\[1 em]k &= \frac{1}{10}&& \\[1 em] \end{aligned} $$

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