32cos^2(x)sin^4(x)=2-cos(2x)-2cos(4x)+cos(6x)

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Solution for 32cos^2(x)sin^4(x)=2-cos(2x)-2cos(4x)+cos(6x) equation: 


Simplifying
32cos2(x) * sin4(x) = 2 + -1cos(2x) + -2cos(4x) + cos(6x)

Multiply cos2 * x
32cos2x * in4s * x = 2 + -1cos(2x) + -2cos(4x) + cos(6x)

Multiply cos2x * in4s
32cin4os3x * x = 2 + -1cos(2x) + -2cos(4x) + cos(6x)

Multiply cin4os3x * x
32cin4os3x2 = 2 + -1cos(2x) + -2cos(4x) + cos(6x)

Remove parenthesis around (2x)
32cin4os3x2 = 2 + -1cos * 2x + -2cos(4x) + cos(6x)

Reorder the terms for easier multiplication:
32cin4os3x2 = 2 + -1 * 2cos * x + -2cos(4x) + cos(6x)

Multiply -1 * 2
32cin4os3x2 = 2 + -2cos * x + -2cos(4x) + cos(6x)

Multiply cos * x
32cin4os3x2 = 2 + -2cosx + -2cos(4x) + cos(6x)

Remove parenthesis around (4x)
32cin4os3x2 = 2 + -2cosx + -2cos * 4x + cos(6x)

Reorder the terms for easier multiplication:
32cin4os3x2 = 2 + -2cosx + -2 * 4cos * x + cos(6x)

Multiply -2 * 4
32cin4os3x2 = 2 + -2cosx + -8cos * x + cos(6x)

Multiply cos * x
32cin4os3x2 = 2 + -2cosx + -8cosx + cos(6x)

Remove parenthesis around (6x)
32cin4os3x2 = 2 + -2cosx + -8cosx + cos * 6x

Reorder the terms for easier multiplication:
32cin4os3x2 = 2 + -2cosx + -8cosx + 6cos * x

Multiply cos * x
32cin4os3x2 = 2 + -2cosx + -8cosx + 6cosx

Combine like terms: -2cosx + -8cosx = -10cosx
32cin4os3x2 = 2 + -10cosx + 6cosx

Combine like terms: -10cosx + 6cosx = -4cosx
32cin4os3x2 = 2 + -4cosx

Solving
32cin4os3x2 = 2 + -4cosx

Solving for variable 'c'.

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

Add '4cosx' to each side of the equation.
32cin4os3x2 + 4cosx = 2 + -4cosx + 4cosx

Combine like terms: -4cosx + 4cosx = 0
32cin4os3x2 + 4cosx = 2 + 0
32cin4os3x2 + 4cosx = 2

Reorder the terms:
-2 + 32cin4os3x2 + 4cosx = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 32cin4os3x2 + 4cosx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 16cin4os3x2 + 2cosx) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 16cin4os3x2 + 2cosx)' equal to zero and attempt to solve:

Simplifying
-1 + 16cin4os3x2 + 2cosx = 0

Solving
-1 + 16cin4os3x2 + 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 + 16cin4os3x2 + 1 + 2cosx = 0 + 1

Reorder the terms:
-1 + 1 + 16cin4os3x2 + 2cosx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16cin4os3x2 + 2cosx = 0 + 1
16cin4os3x2 + 2cosx = 0 + 1

Combine like terms: 0 + 1 = 1
16cin4os3x2 + 2cosx = 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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