$3(x - 3)^2 - 5(6 - 2x) = 0$
$⇔ 3(x^2 - 6x + 9) - 30 + 10x = 0$
$⇔ 3x^2 - 18x + 27 - 30 + 10x = 0$
$⇔ 3x^2 - 8x - 3 = 0$
$⇔ 3x^2 + x - 9x - 3 = 0$
$⇔ x( 3x + 1) - 3( 3x + 1) = 0$
$⇔ (x - 3)(3x + 1) = 0$
⇔ \(\left[{}\begin{matrix}x-3=0\\3x+1=0\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{3}\end{matrix}\right.\)