when you want to solve an equation for a variable, your objective is to get that variable on one side of the equal sign by itself.
5x - 3 = 2x + 12 .........first try to get all the terms with x's on one side
=> 5x - 3 - 2x = 12 .....i subtracted 2x from both sides. now i want to get rid of the -3 on the left
=> 5x - 2x = 12 + 3 .....i added 3 to both sides, now simplify
=> 3x = 15 .................i still don't have x by itself, i have 3 times x on the left, let's get rid of the 3
=> x = 15/3 ...............i divided by 3 on both sides
=> x = 5 ...................i simplified