0=cosx(2cosx-1)

Solution for 0=cosx(2cosx-1) equation:

Simplifying
0 = cosx(2cosx + -1)

Reorder the terms:
0 = cosx(-1 + 2cosx)
0 = (-1 * cosx + 2cosx * cosx)
0 = (-1cosx + 2c2o2s2x2)

Solving
0 = -1cosx + 2c2o2s2x2

Solving for variable 'c'.
Remove the zero:
cosx + -2c2o2s2x2 = -1cosx + 2c2o2s2x2 + cosx + -2c2o2s2x2

Reorder the terms:
cosx + -2c2o2s2x2 = -1cosx + cosx + 2c2o2s2x2 + -2c2o2s2x2

Combine like terms: -1cosx + cosx = 0
cosx + -2c2o2s2x2 = 0 + 2c2o2s2x2 + -2c2o2s2x2
cosx + -2c2o2s2x2 = 2c2o2s2x2 + -2c2o2s2x2

Combine like terms: 2c2o2s2x2 + -2c2o2s2x2 = 0
cosx + -2c2o2s2x2 = 0

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

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}