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Answer 1 · 2017-05-01T19:54:00

#x = (7 pi)/6+2pin#

#x = (11pi)/6+2pin#

#8sinx+5=-2sinx#

Subtract #8sinx# from each side:
#5=-10sinx#

Divide each side by #-10#
#sinx=-1/2#

#x = sin^-1(-1/2)#

I evaluate the #arcsin# term by thinking about the unit circle
#x = (7pi)/6+2pin, (11pi)/6+2pin#

where #n# is an integer.