what is cos^2(x)=2cos(x)

cos^2(x)=2cos(x)   suntract 2cos(x) from both sides

cos^2(x) - 2cos(x) =0    factor

cos(x) [ cos(x) - 2] = 0

Setting the first factor to 0, we have that cos(x) = 0    and this happens at pi/2 + n(pi) ..  (where n is an integer)

Setting the second factor to 0, we have ... cos(x) - 2 = 0   or  (adding 2 to both sides)  cos(x) = 2   which is impossible