cos(x)+cos(3x)+2cos^2(x)=0

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Solution for cos(x)+cos(3x)+2cos^2(x)=0 equation: 


Simplifying
cos(x) + cos(3x) + 2cos2(x) = 0

Multiply cos * x
cosx + cos(3x) + 2cos2(x) = 0

Remove parenthesis around (3x)
cosx + cos * 3x + 2cos2(x) = 0

Reorder the terms for easier multiplication:
cosx + 3cos * x + 2cos2(x) = 0

Multiply cos * x
cosx + 3cosx + 2cos2(x) = 0

Multiply cos2 * x
cosx + 3cosx + 2cos2x = 0

Combine like terms: cosx + 3cosx = 4cosx
4cosx + 2cos2x = 0

Solving
4cosx + 2cos2x = 0

Solving for variable 'c'.

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

Factor out the Greatest Common Factor (GCF), '2cosx'.
2cosx(2 + s) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'cosx' equal to zero and attempt to solve:

Simplifying
cosx = 0

Solving
cosx = 0

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

Simplifying
cosx = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(2 + s)' equal to zero and attempt to solve:

Simplifying
2 + s = 0

Solving
2 + s = 0

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

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

Combine like terms: 2 + -2 = 0
0 + s = 0 + -2
s = 0 + -2

Combine like terms: 0 + -2 = -2
s = -2

Add '-1s' to each side of the equation.
s + -1s = -2 + -1s

Combine like terms: s + -1s = 0
0 = -2 + -1s

Simplifying
0 = -2 + -1s

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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