2x^4+x^3+6x+3>0 solve the system of inequalities

Solve for where it equals 0

use grouping

(2x^4+x^3) + (6x+3) = 0

(x^3) (2x+1) + (3) (2x+1) = 0

(x^3+3) (2x+1) = 0

set equal to zero

x^3+3=0

x^3=-3

x=-∛3

2x+1=0

2x=-1

x=-1/2

now see where the inequality is true

evaluate for x=0

we get 3>0, true

so it it outside the range from - ∛3 to - 1/2

basically

x-1/2

those are the solutionsets