Answer
$x=\frac{2}{3}$
$y=-\frac{1}{2}$
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:
$4-6x+7i+14yi=0$
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 $4-6x=0$, which gives $x=\frac{2}{3}$
The imaginary part $7+14y=0$, which gives $y=-\frac{1}{2}$