(6cosx-1)(cosx+1)=3

Solution for (6cosx-1)(cosx+1)=3 equation:

Simplifying
(6cosx + -1)(cosx + 1) = 3

Reorder the terms:
(-1 + 6cosx)(cosx + 1) = 3

Reorder the terms:
(-1 + 6cosx)(1 + cosx) = 3

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

Combine like terms: -1cosx + 6cosx = 5cosx
(-1 + 5cosx + 6c2o2s2x2) = 3

Solving
-1 + 5cosx + 6c2o2s2x2 = 3

Solving for variable 'c'.

Reorder the terms:
-1 + -3 + 5cosx + 6c2o2s2x2 = 3 + -3

Combine like terms: -1 + -3 = -4
-4 + 5cosx + 6c2o2s2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-4 + 5cosx + 6c2o2s2x2 = 0

Factor a trinomial.
(-4 + -3cosx)(1 + -2cosx) = 0

Subproblem 1
Set the factor '(-4 + -3cosx)' equal to zero and attempt to solve:

Simplifying
-4 + -3cosx = 0

Solving
-4 + -3cosx = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3cosx = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3cosx = 0 + 4
-3cosx = 0 + 4

Combine like terms: 0 + 4 = 4
-3cosx = 4

Divide each side by '-3osx'.
c = -1.333333333o-1s-1x-1

Simplifying
c = -1.333333333o-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 = {-1.333333333o-1s-1x-1, 0.5o-1s-1x-1}