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Answer 1 · 2017-05-03T21:38:28

#x=0, x=(2pi)/3, x=pi, x=(4pi)/3#

#2sin2x+2sinx=0#

Use the double angle identity to simplify #color(blue)(sin(2x))#

#2(color(blue)(2sinxcosx))+2sinx=0#

#4sinxcosx+2sinx=0#

Factor:
#(2sinx)(2cosx+1)=0#

Use zero product rule to determine values:
#2sinx=0#
#sinx=0#

#x=0 , x=pi #

#2cosx+1=0#
#2cosx=-1#
#cosx=(-1)/2#

#x=(2pi)/3 , x=(4pi)/3#