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x4+x3−12<0
Let's find the critical points of the inequality.
x4+x3−12=0
(Use quartic formula)
x=−2.171664,1.653657
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<−2.171664(Doesn't work in original inequality)
−2.171664<x<1.653657(Works in original inequality)
x>1.653657(Doesn't work in original inequality)
Answer:
−2.171664<x<1.653657