6cos^2x-12cosx+6=0

Solution for 6cos^2x-12cosx+6=0 equation:

Simplifying
6cos2x + -12cosx + 6 = 0

Reorder the terms:
6 + -12cosx + 6cos2x = 0

Solving
6 + -12cosx + 6cos2x = 0

Solving for variable 'c'.

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

Add '-6' to each side of the equation.
6 + -12cosx + -6 + 6cos2x = 0 + -6

Reorder the terms:
6 + -6 + -12cosx + 6cos2x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -12cosx + 6cos2x = 0 + -6
-12cosx + 6cos2x = 0 + -6

Combine like terms: 0 + -6 = -6
-12cosx + 6cos2x = -6

Reorder the terms:
6 + -12cosx + 6cos2x = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -12cosx + 6cos2x = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + -2cosx + cos2x) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -2cosx + cos2x)' equal to zero and attempt to solve:

Simplifying
1 + -2cosx + cos2x = 0

Solving
1 + -2cosx + cos2x = 0

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

Add '-1' to each side of the equation.
1 + -2cosx + -1 + cos2x = 0 + -1

Reorder the terms:
1 + -1 + -2cosx + cos2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2cosx + cos2x = 0 + -1
-2cosx + cos2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2cosx + cos2x = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.