Question 969380
Each term has a factor of 3:
{{{15x^2 - 24x - 12}}}
{{{3(5x^2-8x-4)}}}


There are only so few ways to factorize  {{{-4}}}.  Try a few combination of trinomial factorizations for the quadratic factor from the last step.


Look at the possible result for terms of x:


(5  2)(1  2)----------10 and 2, maybe.


(5  4)(1  1)---------5 and 4, NO.


(5  4 )(1   1)----------5 and 4, NO.


Look further at  this:  {{{(5x +- 2)(x+- 2)}}};
You need   {{{-8x}}} and {{{-4}}}.  Decide which signs within the binomials are needed.
......
This is what works:   {{{(5x+2)(x-2)}}}.


Your originally given expression also contained a factor of 3, so to finish your factorization of that, you have
{{{highlight(highlight(3(5x+2)(x-2)))}}}.