$$ \begin{aligned} 6g-\frac{2}{5} &= -g+\frac{3}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot6g-5\cdot\frac{2}{5} &= -5g+5\cdot\frac{3}{5}&& \text{cancel out the denominators} \\[1 em]30g-2 &= -5g+3&& \text{move the $ \color{blue}{ -5g } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]30g+5g &= 3+2&& \text{simplify left and right hand side} \\[1 em]35g &= 5&& \text{ divide both sides by $ 35 $ } \\[1 em]g &= \frac{5}{35}&& \\[1 em]g &= \frac{1}{7}&& \\[1 em] \end{aligned} $$

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