(cosx-1)(2cosx-1)=0

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

Simplifying
(cosx + -1)(2cosx + -1) = 0

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

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

Multiply (-1 + cosx) * (-1 + 2cosx)
(-1(-1 + 2cosx) + cosx(-1 + 2cosx)) = 0
((-1 * -1 + 2cosx * -1) + cosx(-1 + 2cosx)) = 0
((1 + -2cosx) + cosx(-1 + 2cosx)) = 0
(1 + -2cosx + (-1 * cosx + 2cosx * cosx)) = 0
(1 + -2cosx + (-1cosx + 2c2o2s2x2)) = 0

Combine like terms: -2cosx + -1cosx = -3cosx
(1 + -3cosx + 2c2o2s2x2) = 0

Solving
1 + -3cosx + 2c2o2s2x2 = 0

Solving for variable 'c'.

Factor a trinomial.
(1 + -2cosx)(1 + -1cosx) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -1cosx)' equal to zero and attempt to solve:

Simplifying
1 + -1cosx = 0

Solving
1 + -1cosx = 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 + -1cosx = 0 + -1

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

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

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

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