$$ \begin{aligned} 6x-(-3x+3) &= -3+4x&& \text{simplify left and right hand side} \\[1 em]6x+3x-3 &= 4x-3&& \\[1 em]9x-3 &= 4x-3&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]9x-4x &= -3+3&& \text{simplify left and right hand side} \\[1 em]5x &= 0&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{0}{5}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$
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