#### Answer

The solutions are $x=3$ and $x=\pm\dfrac{3}{2}$

#### Work Step by Step

$4x^{3}-12x^{2}=9x-27$
Take all terms to the left side of the equation:
$4x^{3}-12x^{2}-9x+27=0$
Group the first two terms together and the last two terms together:
$(4x^{3}-12x^{2})-(9x-27)=0$
Take out common factor $4x^{2}$ from the first group and common factor $9$ from the second group:
$4x^{2}(x-3)-9(x-3)=0$
Factor out $(x-3)$:
$(x-3)(4x^{2}-9)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-3=0$
$x=3$
$4x^{2}-9=0$
$4x^{2}=9$
$x^{2}=\dfrac{9}{4}$
$\sqrt{x^{2}}=\pm\sqrt{\dfrac{9}{4}}$
$x=\pm\dfrac{3}{2}$
The solutions are $x=3$ and $x=\pm\dfrac{3}{2}$