sin(90-2x)=sin(-523) is another way of writing this.
Therefore 90-2x=-523, 2x=523+90=613 assuming -523 is in degrees. So x=613/2=306.5°.
There are other values for x related to this value. sin(-523)=sin(-523+360)=sin(-163). So 90-2x=-163, 2x=163+90=253°, x=253/2=126.5°, for example.