SOLUTION: 3 sinx - 7= 5 sinx -6 when 0 is less than or equal to x is less than or equal to 360. I need help finding the degrees, just the steps to get there.

Your starting equation is THIS

    3*sin(x) - 7 = 5*sin(x) - 6,    0° <= x < 360°.


Simplify it in standard way

    -7 + 6 = 5*sin(x) - 3*sin(x)  (you collect constant terms in the left side;
                                   you collect sin-terms in the right side).


You get

      -1  = 2*sin(x).


It implies

       sin(x) = -1/2.    (*)


It is a standard equation to determine "x" from the table 
or from a standard "unit circle".

      x = 210° in QIII  (in third quadrant);

      x = 330° in QIV  (in fourth quadrant).


    +------------------------------------------------------------------+
    |  From equation (*), you should get these solutions momentarily   |
    |  from your head: you MUST KNOW IT as the multiplication table.   |
    +------------------------------------------------------------------+


The problem is just solved.

Your original equation has two roots in the given interval.

The solutions are  x = 210° in QIII  and  x = 330° in QIV.