The given equation is:
[tex]x(3x-8)=(3x+6)(x-6)[/tex]
Expand both expressions on the left and right side of the equation and solve the equation for x:
[tex]\begin{gathered} 3x^2-8x=3x^2-18x+6x-36 \\ 3x^2-8x=3x^2-12x-36 \\ \text{Collect like terms:} \\ 3x^2-3x^2-8x+12x=-36 \\ 4x=-36\Rightarrow\frac{4x}{4}=-\frac{36}{4} \\ x=-9 \end{gathered}[/tex]
Hence, the solution set is {-9}. Option (A).
