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

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


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

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

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

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

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

Solving
2 + -3cosx + c2o2s2x2 = 0

Solving for variable 'c'.

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


Subproblem 1
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

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

Simplifying
2 + -1cosx = 0

Solving
2 + -1cosx = 0

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

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

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

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

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

Simplifying
c = 2o-1s-1x-1
Solution
c = {o-1s-1x-1, 2o-1s-1x-1}

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