How do you solve sin 2x equals sin x over 2?

they do have calculators for these questions you know

sin 2x = (sin x)/2

2 sin x cos x - (1/2)sin x = 0

2 sin x(cos x - 1/4) = 0

2 sin x = 0 or cos x - 1/4 = 0

sin x = 0 or cos x = 1/4

in the interval [0, 360)

sin x = 0, when x = 0, 180

cos x = 1/4, when x = 75.52, 284.48

Check: