#### Answer

$x=3$ or $x=-2$
$y=-3$ or $y=3$

#### Work Step by Step

In order to solve the question, the key step here is to compare and observe the individual parts - imaginary and real parts.
bringing all the terms to one side, we have:
$(x^{2}-6)-x+9i-y^{2}i=0$
since the total sum of the real and imaginary parts are equal to $0$, this implies that the sum of the real parts is equal to $0$ and the sum of the imaginary part is equal to $0$
Therefore,
The real part of the expression $(x^{2}-6)-x=0$, can be factorized to $(x-3)(x+2)=0$, which gives $x=3$ or $x=-2$
The imaginary part of the expression $9-y^{2}=0$, can be simplified to $9-y^{2}=0$. The expression can be factorized to $(3-y)(3+y)=0$, which gives $y=-3$ or $y=3$