6cos^2(2x)+cos(2x)=2

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Solution for 6cos^2(2x)+cos(2x)=2 equation: 


Simplifying
6cos2(2x) + cos(2x) = 2

Remove parenthesis around (2x)
6cos2 * 2x + cos(2x) = 2

Reorder the terms for easier multiplication:
6 * 2cos2 * x + cos(2x) = 2

Multiply 6 * 2
12cos2 * x + cos(2x) = 2

Multiply cos2 * x
12cos2x + cos(2x) = 2

Remove parenthesis around (2x)
12cos2x + cos * 2x = 2

Reorder the terms for easier multiplication:
12cos2x + 2cos * x = 2

Multiply cos * x
12cos2x + 2cosx = 2

Reorder the terms:
2cosx + 12cos2x = 2

Solving
2cosx + 12cos2x = 2

Solving for variable 'c'.

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

Reorder the terms:
-2 + 2cosx + 12cos2x = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 2cosx + 12cos2x = 0

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

Ignore the factor 2.

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

Simplifying
-1 + cosx + 6cos2x = 0

Solving
-1 + cosx + 6cos2x = 0

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

Add '1' to each side of the equation.
-1 + cosx + 1 + 6cos2x = 0 + 1

Reorder the terms:
-1 + 1 + cosx + 6cos2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + cosx + 6cos2x = 0 + 1
cosx + 6cos2x = 0 + 1

Combine like terms: 0 + 1 = 1
cosx + 6cos2x = 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.

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