$$ \begin{aligned} 15 &= \frac{4}{7}(4x+35)&& \text{simplify right side} \\[1 em]15 &= \frac{16x+140}{7}&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7\cdot15 &= 7 \cdot \frac{16x+140}{7}&& \text{cancel out the denominators} \\[1 em]105 &= 16x+140&& \text{ swap the left and right side of the equation } \\[1 em]16x+140 &= 105&& \text{ move 140 to the right } \\[1 em]16x &= 105-140&& \\[1 em]16x &= -35&& \text{ divide both sides by $ 16 $ } \\[1 em]x &= -\frac{35}{16}&& \\[1 em] \end{aligned} $$

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