Question

16+8cos(2x)=24cos(x)

Answer 1

\[\large\rm Double ~ angle ~formula:\]\[\large \rm \color{Red}{Cos(2x)= 2\cos^2x -1}\]\[16+8 (\color{Red}{ 2\cos^2x -1})=24\cos(x)\]
distribute parentheses by 8 and then solve the quadratic equation

Answer 2

let say `cos(x)=y`
\[16+8 (\color{Red}{ 2y^2 -1})=24y\]
solve for y