Answer:
x=5
Fast and loose:
Let's isolate -3(x-5)
[tex]-3(x-5) = 2x-10\\-3(x-5) = 2(x-5)[/tex]
Now, if [tex]x=5[/tex], we get [tex]-3(0) = 2(0)[/tex] which is indeed true. If [tex]x\neq 5[/tex], we can divide both sides by (x-5), and get [tex]-3=2[/tex] which is absurd. It means we have no more solutions.
Number crunching:
Let's distribute, bring all terms containging x to the LHS and the rest to the RHS:
[tex]-3x+15-2x=-10\\-5x=-25\\x=\frac{-25}{-5} = 5[/tex]
