How do you do -135+8x=-x+45

...but you started with a different equation.  Note that the minus sign is missing.

-135+8x=-x+45 add 135 to both sides of the equations, add +x to both sides.

9x=180  divide both sides by 9

x=20

$${\mathtt{\,-\,}}{\mathtt{135}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{45}}$$

1.  Subtract $${\mathtt{45}}$$ from both sides:  $${\mathtt{\,-\,}}{\mathtt{135}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{45}} = {\mathtt{x}}$$

2.  Subtract $${\mathtt{45}}$$ from $$-{\mathtt{135}}$$:  $${\mathtt{\,-\,}}{\mathtt{180}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{x}}$$

3.  Subtract $${\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{x}}$$ from both sides:  $$-{\mathtt{180}} = \left(-{\mathtt{7}}\right){\mathtt{\,\times\,}}{\mathtt{x}}$$  

4.  Divide both sides by $$-{\mathtt{7}}$$:  $${\frac{{\mathtt{180}}}{{\mathtt{7}}}}$$

$${\mathtt{x}} = {\frac{{\mathtt{180}}}{{\mathtt{7}}}}$$ or $${\mathtt{25.142\: \!851\: \!428\: \!5}}$$...