SOLUTION: Solve the equation 12sin^3x-20sin^2x+sinx+3=0 given that 2sinx-1 is one factor and x is in between 0 and 360 degrees.

Question 1186338: Solve the equation 12sin^3x-20sin^2x+sinx+3=0 given that 2sinx-1 is one factor and x is in between 0 and 360 degrees.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let y = sinx.
===> The equation can be represented as . From the hint, 2y - 1 is a factor of the left-hand side.

===> after dividing both sides by 2y - 1.
===> (3y + 1)(2y - 3) = 0 ===> y = -1/3 or 3/2.

Since y = sinx = 3/2 has no solution, we solve y = sinx = -1/3.

===> x = , (both in degrees).

Finally the solutions for 2sinx - 1 = 0, or sinx = 1/2, are x = , (both in degrees).

All the values in red ink are the solutions to the original equation.
RELATED QUESTIONS
Solve for all values of x if x is measured in degrees. 2cos^2x=3sinx 2(1-sin^2x)=3sinx (answered by stanbon)

solve 12sin^2(x)+2sin(x)-2=0 where x is in radians between 0 and... (answered by Alan3354)

solve 12sin^2(x)+2sin(x)-2=0 for all solutions where x is in radians between 0 and... (answered by lwsshak3)

Can someone help verify this: consider the equation (5/2) cos2x - 1/2 =3 sinx. A) Put... (answered by Alan3354)

i)- Solve the following equations for 0� < x < 360�. a) 2sinx cosx = 3 sinx b) (answered by Fombitz)

What are all the solutions of sinx - radical 3 sinx = 0 if 0 degrees is lees than x and x (answered by lwsshak3)

If cosx=-3/5, and x is in between 180 and 360 degrees, find the value of... (answered by Boreal,ikleyn)

Hello, Please hep me to solve this problem: Find all exact value solutions [o,360) for... (answered by robertb)

Question 1. 2cosx^4 -3cosx^2 +1=0 Question 2. 4sinx^4 +3sinx^2 -1=0 Question 3.... (answered by Alan3354)