Question 174223
{{{(6k-3)/(2k+7)=(3k-2)/(k+5)}}}  
First thing to do is clear the denominators. We will need to come back to this step later to verify our 'answer' is a valid one. So cross multiply and clear them.
{{{(6k-3)(k+5)=(3k-2)(2k+7)}}}  Now expand
{{{6k^2 +30k - 3k - 15 = 6k^2 + 21k -4k -14}}} simplify
{{{6k^2 + 27k - 15 = 6k^2 + 17k - 14}}} collect like terms 
{{{10k = 1}}}
{{{k = 1/10}}}

Will that value if k make either of the original denominators = 0? No it won't so, 1/10 is a valid possibility.

Check the original equation using x=(1/10) and verify it satisfies the equation. Does it?

{{{(0.6-3)/(0.2 + 7) = ( 0.3-2)/(0.1+5)}}}
{{{(-2.4)/(7.2) = (-1.7)/(5.1)}}}
{{{-1/3 = -1/3}}} which is true. so the answer is 1/10