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

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

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

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

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

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

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

Solving
1 + 3cosx + 2c2o2s2x2 = 0

Solving for variable 'c'.

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

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

Simplifying
1 + cosx = 0

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

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

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

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

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