solve 4sin^2 x-4sinx-3=0 for 0<=x<=360

solve 4sin^2 x-4sinx-3=0 for 0<=x<=360

Let y=sinx and solve for y

$$\begin{array}{rll}
4y^2-4y-3&=&0\\\\
4y^2+2y-6y-3&=&0\\\\
2y(2y+1)-3(2y+1)&=&0\\\\
(2y-3)(2y+1)&=&0\\\\
\end{array}$$

$$\begin{array}{rllllrll}
so\qquad y&=&3/2\quad &or&\quad y&=&-1/2\\\\
sinx&=&3/2\quad &or&\quad sinx&=&-1/2\\\\
No\:\: solution&& &or&\quad sinx&=&-1/2\\\\
\end{array}$$

sinx is negative so x must be in the 3rd or forth quadrant

x=180+30=210 degrees  or   x=360-30=330degrees

x=210 degrees of 330 degrees

I have not checked these answers.  YOu can check by plugging the numbers back into the formula and checking that they work.

If you have questions, feel free to ask.