(2cosx-1)(3+2cosx)=0

Solution for (2cosx-1)(3+2cosx)=0 equation:

Simplifying
(2cosx + -1)(3 + 2cosx) = 0

Reorder the terms:
(-1 + 2cosx)(3 + 2cosx) = 0

Multiply (-1 + 2cosx) * (3 + 2cosx)
(-1(3 + 2cosx) + 2cosx * (3 + 2cosx)) = 0
((3 * -1 + 2cosx * -1) + 2cosx * (3 + 2cosx)) = 0
((-3 + -2cosx) + 2cosx * (3 + 2cosx)) = 0
(-3 + -2cosx + (3 * 2cosx + 2cosx * 2cosx)) = 0
(-3 + -2cosx + (6cosx + 4c2o2s2x2)) = 0

Combine like terms: -2cosx + 6cosx = 4cosx
(-3 + 4cosx + 4c2o2s2x2) = 0

Solving
-3 + 4cosx + 4c2o2s2x2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-3 + -2cosx)(1 + -2cosx) = 0

Subproblem 1
Set the factor '(-3 + -2cosx)' equal to zero and attempt to solve:

Simplifying
-3 + -2cosx = 0

Solving
-3 + -2cosx = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2cosx = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2cosx = 0 + 3
-2cosx = 0 + 3

Combine like terms: 0 + 3 = 3
-2cosx = 3

Divide each side by '-2osx'.
c = -1.5o-1s-1x-1

Simplifying
c = -1.5o-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 = {-1.5o-1s-1x-1, 0.5o-1s-1x-1}