a: \(\left(2x-1\right)\left(x^2-x+1\right)+x^2\left(3-2x\right)=2\)
=>\(2x^3-2x^2+2x-x^2+x+1+3x^2-2x^3=2\)
=>3x+1=2
=>3x=1
=>\(x=\dfrac{1}{3}\)
b: \(3\left(1-4x\right)\left(x-2\right)+4\left(3x+1\right)\left(x+2\right)=24\)
=>\(3\left(x-2-4x^2+8x\right)+4\left(3x^2+6x+x+2\right)=24\)
=>\(3\left(-4x^2+9x-2\right)+4\left(3x^2+7x+2\right)=24\)
=>\(-12x^2+27x-6+12x^2+28x+8=24\)
=>55x+2=24
=>55x=22
=>\(x=\dfrac{22}{55}=\dfrac{2}{5}\)
c: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)-x^3-8x\left(x+2\right)=6\)
=>\(\left(x^2+3x+2\right)\left(x+3\right)-x^3-8x\left(x+2\right)=6\)
=>\(x^3+3x^2+3x^2+9x+2x+6-x^3-8x^2-16x=6\)
=>\(-2x^2-5x=0\)
=>\(x\left(2x+5\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{5}{2}\end{matrix}\right.\)
d: \(\left(x+1\right)\left(x^2+2x+4\right)-x^2\left(x+3\right)+8=0\)
=>\(x^3+2x^2+4x+x^2+2x+4-x^3-3x^2+8=0\)
=>\(6x+12=0\)
=>6x=-12
=>x=-2
