6cos(2x)+2=4cos^2x

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Solution for 6cos(2x)+2=4cos^2x equation: 


Simplifying
6cos(2x) + 2 = 4cos2x

Remove parenthesis around (2x)
6cos * 2x + 2 = 4cos2x

Reorder the terms for easier multiplication:
6 * 2cos * x + 2 = 4cos2x

Multiply 6 * 2
12cos * x + 2 = 4cos2x

Multiply cos * x
12cosx + 2 = 4cos2x

Reorder the terms:
2 + 12cosx = 4cos2x

Solving
2 + 12cosx = 4cos2x

Solving for variable 'c'.

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

Add '-4cos2x' to each side of the equation.
2 + 12cosx + -4cos2x = 4cos2x + -4cos2x

Combine like terms: 4cos2x + -4cos2x = 0
2 + 12cosx + -4cos2x = 0

Add '-2' to each side of the equation.
2 + 12cosx + -2 + -4cos2x = 0 + -2

Reorder the terms:
2 + -2 + 12cosx + -4cos2x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 12cosx + -4cos2x = 0 + -2
12cosx + -4cos2x = 0 + -2

Combine like terms: 0 + -2 = -2
12cosx + -4cos2x = -2

Reorder the terms:
2 + 12cosx + -4cos2x = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 12cosx + -4cos2x = 0

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

Ignore the factor 2.

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

Simplifying
1 + 6cosx + -2cos2x = 0

Solving
1 + 6cosx + -2cos2x = 0

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

Add '-1' to each side of the equation.
1 + 6cosx + -1 + -2cos2x = 0 + -1

Reorder the terms:
1 + -1 + 6cosx + -2cos2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6cosx + -2cos2x = 0 + -1
6cosx + -2cos2x = 0 + -1

Combine like terms: 0 + -1 = -1
6cosx + -2cos2x = -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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