This will be easier to write, and a lot easier to read, if we temporarily
use another symbol ... say, 'Q' ... to represent ' sin(2x) ' .
Here we go:
Original equation: Q² - 0.5 Q = 0
Factor the left side: Q (Q - 0.5) = 0
This equation is true if either factor is zero:
-- If Q=0, then sin(2x) = 0
2x = 0°, 180°, 360°
x = 0°, 90°, 180°
-- If (Q-0.5) = 0, then Q = 0.5
sin(2x) = 0.5
2x = 30°, 150°
x = 15°, 75°
The whole collection of solutions
between 0° and 360° :
x = 0°, 15°, 75°, 90°, 180° .