$$ \begin{aligned} 13x-5+8x-3 &= 12x-7+10x-15&& \text{simplify left and right hand side} \\[1 em]21x-8 &= 22x-22&& \text{move the $ \color{blue}{ 22x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]21x-22x &= -22+8&& \text{simplify left and right hand side} \\[1 em]-x &= -14&& \text{switch signs on both sides} \\[1 em]x &= 14&& \\[1 em] \end{aligned} $$

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