\(PT\Leftrightarrow\left(x-\frac{2}{3}\right)\left(3x^2+6x+9\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{2}{3}=0\\3x^2+6x+9=0\left(vônghiệm\right)\end{cases}}\)
\(\Rightarrow x=\frac{2}{3}\)
\(3x^3+4x^2+5x-6=0\)
\(\Leftrightarrow3x^3-2x^2+6x^2-4x+9x-6=0\)
\(\Leftrightarrow x^2\left(3x-2\right)+2x\left(3x-2\right)+3\left(3x-2\right)=0\)
\(\Leftrightarrow\left(3x-2\right)\left(x^2+2x+3\right)=0\)
Mà \(x^2+2x+3=\left(x+1\right)^2+2>0\left(\forall x\right)\)
\(\Rightarrow3x-2=0\Leftrightarrow x=\frac{2}{3}\)
Tập nghiệm của pt: \(S=\left\{\frac{2}{3}\right\}\)
