Answer:
[tex]b=-\frac{-mx-2x+2m-60}{x};\quad \:x\ne \:0[/tex]
Step-by-step explanation:
Given the expression
[tex]\left(x-2\right)\left(x-m\right)=x^2-bx+60[/tex]
switch sides
[tex]x^2-bx+60=\left(x-2\right)\left(x-m\right)[/tex]
subtract x² from both sides
[tex]x^2-bx+60-x^2=\left(x-2\right)\left(x-m\right)-x^2[/tex]
simplify
[tex]-bx+60=-mx-2x+2m[/tex]
subtract 60 from both sides
[tex]-bx+60-60=-mx-2x+2m-60[/tex]
simplify
[tex]-bx=-mx-2x+2m-60[/tex]
subtract x from both sides; x≠0
[tex]\frac{-bx}{-x}=-\frac{mx}{-x}-\frac{2x}{-x}+\frac{2m}{-x}-\frac{60}{-x};\quad \:x\ne \:0[/tex]
simplify
[tex]b=-\frac{-mx-2x+2m-60}{x};\quad \:x\ne \:0[/tex]
Thus,
[tex]b=-\frac{-mx-2x+2m-60}{x};\quad \:x\ne \:0[/tex]
