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

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


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

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

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

Multiply (1 + 2cosx) * (-2 + cosx)
(1(-2 + cosx) + 2cosx * (-2 + cosx)) = 0
((-2 * 1 + cosx * 1) + 2cosx * (-2 + cosx)) = 0
((-2 + 1cosx) + 2cosx * (-2 + cosx)) = 0
(-2 + 1cosx + (-2 * 2cosx + cosx * 2cosx)) = 0
(-2 + 1cosx + (-4cosx + 2c2o2s2x2)) = 0

Combine like terms: 1cosx + -4cosx = -3cosx
(-2 + -3cosx + 2c2o2s2x2) = 0

Solving
-2 + -3cosx + 2c2o2s2x2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-1 + -2cosx)(2 + -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 '(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 = {-0.5o-1s-1x-1, 2o-1s-1x-1}

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