cos(8x)(2cos(x)+1)=0

Solution for cos(8x)(2cos(x)+1)=0 equation:

Simplifying
cos(8x)(2cos(x) + 1) = 0

Remove parenthesis around (8x)
cos * 8x(2cos(x) + 1) = 0

Multiply cos * x
cos * 8x(2cosx + 1) = 0

Reorder the terms:
cos * 8x(1 + 2cosx) = 0

Reorder the terms for easier multiplication:
8cos * x(1 + 2cosx) = 0

Multiply cos * x
8cosx(1 + 2cosx) = 0
(1 * 8cosx + 2cosx * 8cosx) = 0
(8cosx + 16c2o2s2x2) = 0

Solving
8cosx + 16c2o2s2x2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '8cosx'.
8cosx(1 + 2cosx) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'cosx' equal to zero and attempt to solve:

Simplifying
cosx = 0

Solving
cosx = 0

Move all terms containing c to the left, all other terms to the right.

Simplifying
cosx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + 2cosx)' equal to zero and attempt to solve:

Simplifying
1 + 2cosx = 0

Solving
1 + 2cosx = 0

Move all terms containing c to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2cosx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2cosx = 0 + -1
2cosx = 0 + -1

Combine like terms: 0 + -1 = -1
2cosx = -1

Divide each side by '2osx'.
c = -0.5o-1s-1x-1

Simplifying
c = -0.5o-1s-1x-1
Solution
c = {-0.5o-1s-1x-1}