$$ \begin{aligned} 4x+9 &= 5x+0&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]4x-5x &= -9&& \text{simplify left side} \\[1 em]-x &= -9&& \text{switch signs on both sides} \\[1 em]x &= 9&& \\[1 em] \end{aligned} $$