The set of all values of $k>-1$, for which the equation $\left(3 x^2+4 x+3\right)^2-(k+1)\left(3 x^2+4 x+3\right)\left(3 x^2+4 x+2\right)+ k\left(3 x^2+4 x+2\right)^2=0$ has real roots, is i.
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