Lời giải:
PT $\Leftrightarrow (8x^3-36x^2+54x-27)-(8x^3-2x+12x^2-3)=-24$
$\Leftrightarrow -48x^2+56x-24=-24$
$\Leftrightarrow -48x^2+56x=0$
$\Leftrightarrow 8x(7-6x)=0$
$\Leftrightarrow x=0$ hoặc $7-6x=0$
$\Leftrightarrow x=0$ hoặc $x=\frac{7}{6}$
\(\left(2x-3\right)^3-\left(2x+3\right)\left(4x^2-1\right)=-24\)
\(8x^3-18x^2+27x-27-\left(8x^3-2x+12x^2-3\right)\) =-24
\(8x^3-18x^2+27x-27-8x^3+2x-12x^2-3\) = -24
\(-30x^2+29x-30=-24\)
\(-30x^2+29x=6\)\(x\left(-30x+29\right)=6\)
Ta có: \(\left(2x-3\right)^3-\left(2x+3\right)\left(4x^2-1\right)=-24\)
\(\Leftrightarrow8x^2-36x^2+54x-27-8x^3+2x-12x^2+3=-24\)
\(\Leftrightarrow-48x^2+56x=0\)
\(\Leftrightarrow-8x\left(6x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{7}{6}\end{matrix}\right.\)