How do you solve 2sin^2xtanx=tanx

please help me solve this questions i dont know what to do:)

Subtract both sides by tan(x):

2sin²(x)tan(x) - tan(x) = 0

Then, factor out the GCF of tan(x):

tan(x)(2sin²(x) - 1) = 0

Finally, by zero-product identity:

tan(x) = 0 and 2sin²(x) - 1 = 0
tan(x) = 0 and sin²(x) = ½
tan(x) = 0 and sin(x) = ±√(½)
tan(x) = 0 and sin(x) = 1/√(2) and sin(x) = -1/√(2)
x = arctan(0) and x = arcsin(1/√2) and x = arcsin(-1/√(2))
x = 0, ±π, ±3π/4, ±π/4

I hope this helps!