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

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


Simplifying
32sin2(x) * cos4(x) = -1cos(6x) + -2cos(4x) + cos(2x) + 2

Multiply in2s * x
32in2sx * cos4 * x = -1cos(6x) + -2cos(4x) + cos(2x) + 2

Multiply in2sx * cos4
32cin2os5x * x = -1cos(6x) + -2cos(4x) + cos(2x) + 2

Multiply cin2os5x * x
32cin2os5x2 = -1cos(6x) + -2cos(4x) + cos(2x) + 2

Remove parenthesis around (6x)
32cin2os5x2 = -1cos * 6x + -2cos(4x) + cos(2x) + 2

Reorder the terms for easier multiplication:
32cin2os5x2 = -1 * 6cos * x + -2cos(4x) + cos(2x) + 2

Multiply -1 * 6
32cin2os5x2 = -6cos * x + -2cos(4x) + cos(2x) + 2

Multiply cos * x
32cin2os5x2 = -6cosx + -2cos(4x) + cos(2x) + 2

Remove parenthesis around (4x)
32cin2os5x2 = -6cosx + -2cos * 4x + cos(2x) + 2

Reorder the terms for easier multiplication:
32cin2os5x2 = -6cosx + -2 * 4cos * x + cos(2x) + 2

Multiply -2 * 4
32cin2os5x2 = -6cosx + -8cos * x + cos(2x) + 2

Multiply cos * x
32cin2os5x2 = -6cosx + -8cosx + cos(2x) + 2

Remove parenthesis around (2x)
32cin2os5x2 = -6cosx + -8cosx + cos * 2x + 2

Reorder the terms for easier multiplication:
32cin2os5x2 = -6cosx + -8cosx + 2cos * x + 2

Multiply cos * x
32cin2os5x2 = -6cosx + -8cosx + 2cosx + 2

Reorder the terms:
32cin2os5x2 = 2 + -6cosx + -8cosx + 2cosx

Combine like terms: -6cosx + -8cosx = -14cosx
32cin2os5x2 = 2 + -14cosx + 2cosx

Combine like terms: -14cosx + 2cosx = -12cosx
32cin2os5x2 = 2 + -12cosx

Solving
32cin2os5x2 = 2 + -12cosx

Solving for variable 'c'.

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

Add '12cosx' to each side of the equation.
32cin2os5x2 + 12cosx = 2 + -12cosx + 12cosx

Combine like terms: -12cosx + 12cosx = 0
32cin2os5x2 + 12cosx = 2 + 0
32cin2os5x2 + 12cosx = 2

Reorder the terms:
-2 + 32cin2os5x2 + 12cosx = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 32cin2os5x2 + 12cosx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 16cin2os5x2 + 6cosx) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 16cin2os5x2 + 6cosx)' equal to zero and attempt to solve:

Simplifying
-1 + 16cin2os5x2 + 6cosx = 0

Solving
-1 + 16cin2os5x2 + 6cosx = 0

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

Add '1' to each side of the equation.
-1 + 16cin2os5x2 + 1 + 6cosx = 0 + 1

Reorder the terms:
-1 + 1 + 16cin2os5x2 + 6cosx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16cin2os5x2 + 6cosx = 0 + 1
16cin2os5x2 + 6cosx = 0 + 1

Combine like terms: 0 + 1 = 1
16cin2os5x2 + 6cosx = 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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