$$ \begin{aligned} 13x-5(2x-1) &= 4x+3&& \text{simplify left side} \\[1 em]13x-(10x-5) &= 4x+3&& \\[1 em]13x-10x+5 &= 4x+3&& \\[1 em]3x+5 &= 4x+3&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]3x-4x &= 3-5&& \text{simplify left and right hand side} \\[1 em]-x &= -2&& \text{switch signs on both sides} \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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