Verified answer

You really should learn to type a statement so it says what you mean. A math statement must have exactly one way to interpret it.

cos^2 * 6x is meaningless.

Making assumptions about where parentheses should be,

2cos^2(6x) - 1 = 0

cos^2(6x) = 1/2

cos(6x) = 1/√2

6x = pi/4 + 2npi or 6x = 7pi/4 + 2npi for all integers, n

x = pi/24 + npi/3 or x = 7pi/24 + npi/3 for all integer, n

Let 6x = t

2 * cos(6x)^2 - 1 = 0

2 * cos(t)^2 - 1 = 0

2 * cos(t)^2 = 1

cos(t)^2 = 1/2

cos(t) = -sqrt(2)/2 , sqrt(2)/2

t = pi/4 , 3pi/4 , 5pi/4 , 7pi/4 , 9pi/4 , ...

t = pi/4 + (pi/2) * k

k is an integer

6x = (pi/4) * (1 + 2k)

x = (pi/24) * (1 + 2k)

There you go.