This isn't an inequality, it's an equation. We can divide through by m: m(2m^2+7m-4)=0. The quadratic factorises: m(2m-1)(m+4)=0. Clearly the solutions are m=0, 1/2 and -4. Replace = with <, and a different picture emerges. If m<-4 then the inequality is true; if m=-4 the inequality is false because this value of m makes the expression =0. If the inequality was <= then it would be true. Now take -4<m<0. The inequality (<0) would be false, because m(2m-1) would produce a positive number (minus times minus is plus) and m+4 is positive. If the inequality was <=, then m=0 would make the inequality true. Now take 0<m<1/2. The inequality is true, because 2m-1 is negative and the other two terms are positive. When m=1/2 the inequality <= or >= would be true. When m>1/2, the inequality is false. Similar tests over various ranges for m can be carried out to check out other inequalities (>, =>, <>).