20cos^3(4x)-40sin^2(4x)cos(4x)=0

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Solution for 20cos^3(4x)-40sin^2(4x)cos(4x)=0 equation:


Simplifying
20cos3(4x) + -40sin2(4x) * cos(4x) = 0

Remove parenthesis around (4x)
20cos3 * 4x + -40sin2(4x) * cos(4x) = 0

Reorder the terms for easier multiplication:
20 * 4cos3 * x + -40sin2(4x) * cos(4x) = 0

Multiply 20 * 4
80cos3 * x + -40sin2(4x) * cos(4x) = 0

Multiply cos3 * x
80cos3x + -40sin2(4x) * cos(4x) = 0

Remove parenthesis around (4x)
80cos3x + -40in2s * 4x * cos(4x) = 0

Remove parenthesis around (4x)
80cos3x + -40in2s * 4x * cos * 4x = 0

Reorder the terms for easier multiplication:
80cos3x + -40 * 4 * 4in2s * x * cos * x = 0

Multiply -40 * 4
80cos3x + -160 * 4in2s * x * cos * x = 0

Multiply -160 * 4
80cos3x + -640in2s * x * cos * x = 0

Multiply in2s * x
80cos3x + -640in2sx * cos * x = 0

Multiply in2sx * cos
80cos3x + -640cin2os2x * x = 0

Multiply cin2os2x * x
80cos3x + -640cin2os2x2 = 0

Reorder the terms:
-640cin2os2x2 + 80cos3x = 0

Solving
-640cin2os2x2 + 80cos3x = 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), '80cos2x'.
80cos2x(-8in2x + s) = 0

Ignore the factor 80.

Subproblem 1

Set the factor 'cos2x' equal to zero and attempt to solve: Simplifying cos2x = 0 Solving cos2x = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cos2x = 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 '(-8in2x + s)' equal to zero and attempt to solve: Simplifying -8in2x + s = 0 Solving -8in2x + s = 0 Move all terms containing c to the left, all other terms to the right. Add '8in2x' to each side of the equation. -8in2x + 8in2x + s = 0 + 8in2x Combine like terms: -8in2x + 8in2x = 0 0 + s = 0 + 8in2x s = 0 + 8in2x Remove the zero: s = 8in2x Add '-1s' to each side of the equation. s + -1s = 8in2x + -1s Combine like terms: s + -1s = 0 0 = 8in2x + -1s Simplifying 0 = 8in2x + -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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