Question 1082260

hi can you help me understand how multiplying fractions by LCM simplifies this linear equation ? 
even though i know how to do it but i dont understand how it works
this is a direct copy from a book
step 1{{{ 3x/2 = x/5 - 39/5}}}
step 2{{{ (10)3x/2 = (10)x/5 - (10) 39/5}}}
result {{{ 15x = 2x - 78}}}
{{{ x = -6}}}

my main problem with this is that when we multiply all the fractions by 10 it also has effects on the term x so i dont understand why it dosent change the result if you can please explain step by step how it works thanks.
<pre>{{{3x/2 = x/5 - 39/5}}}
{{{10(3x/2) = 10(x/5) - 10(39/5)}}} --------- Multiplying EACH TERM by LCD, 10
{{{5cross(10)(3x/cross(2)) = 2cross(10)(x/cross(5)) - 2cross(10)(39/cross(5))}}} ---- Cancelling denominators with numerators
5(3x) = 2(x) - 2(39)
15x = 2x - 78
15x - 2x = 78
13x = 78
{{{highlight_green(matrix(1,3, x, "=", - 6))}}}