16sin^5(x)-20sin^3(x)+5sin(x)

[latex]16sin^5x-20sin^3x+5sinx=0[/latex] [latex]5sinx-20*( \frac{3sinx-sin3x}{4} )+16sin^5x=0[/latex] [latex]5sinx-20*( \frac{3sinx}{4} - \frac{sin3x}{4} )+16sin^5x=0[/latex] [latex]5sinx-20*( \frac{3sinx}{4} - \frac{sin3x}{4} )+16*( \frac{10sinx-5sin3x+sin5x}{16} )=0[/latex] [latex]5sinx-20*( \frac{3sinx}{4} - \frac{sin3x}{4})+16*(\frac{5sinx}{8}-\frac{5sin3x}{16}+\frac{sin5x}{16})=0 [/latex] [latex]5sinx+(5sin3x-15sinx)+16*(\frac{5sinx}{8}-\frac{5sin3x}{16}+\frac{sin5x}{16})=0 [/latex] [latex]5sinx-15sinx+5sin3x+(10sinx-5sin3x+sin5x)=0[/latex] [latex]sin5x=0[/latex] [latex]5x= \pi n[/latex]; n∈Z [latex]x= \frac{ \pi n}{5} [/latex]; n∈Z