Find all solutions to the equation in the interval 02 pi 8co

Find all solutions to the equation in the interval [0,2 pi). 8cos^2(x) = 32 cos(x) + 24 = 0

Solution

8cos²(x) -32cos(x) +24=0

8[cos²(x) -4cos(x) +3]=0

cos²(x) -4cos(x) +3=0

cos²(x) -3cos(x) -cos(x) +3=0

cos(x) (cos(x) -3) -1(cos(x) -3)=0

(cos(x)-3)(cos(x)-1)=0

cos(x)=3 no solution

cos(x)=1 =>x=0

only solution is x=0