`(x - 2)^3 + (2x +1)^3 - 9(x + 1)^3 = -16`
`<=>(x-2)^3-(x+1)^3+(2x+1)^3-8(x+1)^3=-16`
`<=>(x-2)^3-(x+1)^3+(2x+1)^3-[2(x+1)]^3`
`<=>(x-2-x-1)[(x-2)^2+(x-2)(x+1)+(x+1)^2]+(2x+1-2x-2)[(2x+1)^2+(2x+1)(2x+2)+(2x+2)^2]+16=0`
`<=>-3.(x^2-4x+4+x^2-x-2+x^2+2x+1)-(4x^2+4x+1+4x^2+6x+2+4x^2+8x+4)+16=0`
`<=>-3.(3x^2-3x+3)-(12x^2+18x+7)+16=0`
`<=>-9x^2+9x-9-12x^2-18x-7+16=0`
`<=>-21x^2-9x-16+16=0`
`<=>-21x^2-9x=0`
`<=>7x^2+3x=0`
`<=>x(7x+3)=0`
`=>` \(\left[ \begin{array}{l}x=0\\7x+3=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=0\\x=-\dfrac{3}{7}\end{array} \right.\)