Precalculus, Chapter 5, 5.3, Section 5.3, Problem 33

Find all solutions to the equation 2cos^2(x)+cos(x)-1=0 in the interval [0,2pi).
2cos^2(x)+cos(x)-1=0
(2cos(x)-1)(cos(x)+1)=0
Set each factor equal to zero and solve for the x value(s).
2cos(x)-1=0
2cos(x)=1
cos(x)=1/2
x=pi/3,x=(5pi)/3

cos(x)+1=0
cos(x)=-1
x=pi