STEP - BY - STEP EXPLANATION
What to find?
The values of x.
Given:
[tex]sin^2x+sinx=0[/tex]
Step 1
Factorize sinx.
[tex]sinx(sinx+1)=0[/tex]
Step 2
Equate each to zero.
[tex]\begin{gathered} sinx=0 \\ \\ sinx+1=0 \\ \Rightarrow sinx=-1 \end{gathered}[/tex][tex]\begin{gathered} sinx=0 \\ \Rightarrow x=2\pi n \\ \Rightarrow x=0,\text{ 2}\pi \end{gathered}[/tex][tex]\begin{gathered} sinx=-1 \\ \Rightarrow x=\frac{3\pi}{2}+2\pi n \\ \\ x=\frac{3\pi}{2} \end{gathered}[/tex]
ANSWER
[tex]x=0,\text{ 2}\pi,\text{ }\frac{3\pi}{2}[/tex]
