Question 908572
Looks like the function is negative between {{{x=-4}}} and {{{x=2}}}.
{{{graph(300,300,-10,10,-10,10,2x^2+5x-12)}}}
Check to see if  {{{x=-4}}} satisfies the inequality.
{{{graph(300,300,-5,3,-4,4,2x^2+5x-12)}}}
{{{2x^2+5x-12<0}}}
{{{2(-4)^2+5(-4)-12<0}}}
{{{2(16)-20-12<0}}}
{{{32-32<0}}}
{{{0<0}}}
No, so {{{x=-4}}} is not in the solution set.
{{{x=-3}}}
{{{x=-2}}}
{{{x=-1}}}
{{{x=0}}}
{{{x=1}}}
5 integers in total