$$ \begin{aligned} 9x+6 &= 10x-3&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]9x-10x &= -3-6&& \text{simplify left and right hand side} \\[1 em]-x &= -9&& \text{switch signs on both sides} \\[1 em]x &= 9&& \\[1 em] \end{aligned} $$