a.
\(x\left(x^2-1\right)+x^2\left(3-x\right)=0\)
\(\Leftrightarrow x^3-x+3x^2-x^3=0\)
\(\Leftrightarrow3x^2-x=0\)
\(\Leftrightarrow x\left(3x-1\right)=0\)
\(\Leftrightarrow x=0\) hoặc \(3x-1=0\)
\(\Leftrightarrow x=0\) hoặc \(x=\dfrac{1}{3}\)
b.
\(3x\left(x-5\right)+6\left(5-x\right)=0\)
\(\Leftrightarrow3x\left(x-5\right)-6\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(3x-6\right)=0\)
\(\Leftrightarrow x-5=0\) hoặc \(3x-6=0\)
\(\Leftrightarrow x=5\) hoặc \(x=2\)
c.
\(\left(x-1\right)\left(x^2+x+1\right)+9=0\)
\(\Leftrightarrow x^3+x^2+x-x^2-x-1+9=0\)
\(\Leftrightarrow x^3+8=0\)
\(\Leftrightarrow x^3=-8=\left(-2\right)^3\)
\(\Rightarrow x=-2\)
