sin(5*A)=SinA*(16sin^4A-20Sin^2A+5)

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Solution for sin(5*A)=SinA*(16sin^4A-20Sin^2A+5) equation: 


Simplifying
sin(5A) = SinA(16sin4A + -20Sin2A + 5)

Remove parenthesis around (5A)
ins * 5A = SinA(16sin4A + -20Sin2A + 5)

Reorder the terms for easier multiplication:
5ins * A = SinA(16sin4A + -20Sin2A + 5)

Multiply ins * A
5insA = SinA(16sin4A + -20Sin2A + 5)

Reorder the terms:
5insA = inAS(5 + -20in2AS + 16in4sA)
5insA = (5 * inAS + -20in2AS * inAS + 16in4sA * inAS)
5insA = (5inAS + -20i2n3A2S2 + 16i2n5sA2S)

Solving
5insA = 5inAS + -20i2n3A2S2 + 16i2n5sA2S

Solving for variable 'i'.

Reorder the terms:
-5inAS + 5insA + 20i2n3A2S2 + -16i2n5sA2S = 5inAS + -20i2n3A2S2 + 16i2n5sA2S + -5inAS + 20i2n3A2S2 + -16i2n5sA2S

Reorder the terms:
-5inAS + 5insA + 20i2n3A2S2 + -16i2n5sA2S = 5inAS + -5inAS + -20i2n3A2S2 + 20i2n3A2S2 + 16i2n5sA2S + -16i2n5sA2S

Combine like terms: 5inAS + -5inAS = 0
-5inAS + 5insA + 20i2n3A2S2 + -16i2n5sA2S = 0 + -20i2n3A2S2 + 20i2n3A2S2 + 16i2n5sA2S + -16i2n5sA2S
-5inAS + 5insA + 20i2n3A2S2 + -16i2n5sA2S = -20i2n3A2S2 + 20i2n3A2S2 + 16i2n5sA2S + -16i2n5sA2S

Combine like terms: -20i2n3A2S2 + 20i2n3A2S2 = 0
-5inAS + 5insA + 20i2n3A2S2 + -16i2n5sA2S = 0 + 16i2n5sA2S + -16i2n5sA2S
-5inAS + 5insA + 20i2n3A2S2 + -16i2n5sA2S = 16i2n5sA2S + -16i2n5sA2S

Combine like terms: 16i2n5sA2S + -16i2n5sA2S = 0
-5inAS + 5insA + 20i2n3A2S2 + -16i2n5sA2S = 0

Factor out the Greatest Common Factor (GCF), 'inA'.
inA(-5S + 5s + 20in2AS2 + -16in4sAS) = 0


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

Simplifying
inA = 0

Solving
inA = 0

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

Simplifying
inA = 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 '(-5S + 5s + 20in2AS2 + -16in4sAS)' equal to zero and attempt to solve:

Simplifying
-5S + 5s + 20in2AS2 + -16in4sAS = 0

Reorder the terms:
-5S + 20in2AS2 + -16in4sAS + 5s = 0

Solving
-5S + 20in2AS2 + -16in4sAS + 5s = 0

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

Add '5S' to each side of the equation.
-5S + 20in2AS2 + -16in4sAS + 5S + 5s = 0 + 5S

Reorder the terms:
-5S + 5S + 20in2AS2 + -16in4sAS + 5s = 0 + 5S

Combine like terms: -5S + 5S = 0
0 + 20in2AS2 + -16in4sAS + 5s = 0 + 5S
20in2AS2 + -16in4sAS + 5s = 0 + 5S
Remove the zero:
20in2AS2 + -16in4sAS + 5s = 5S

Add '-5s' to each side of the equation.
20in2AS2 + -16in4sAS + 5s + -5s = 5S + -5s

Combine like terms: 5s + -5s = 0
20in2AS2 + -16in4sAS + 0 = 5S + -5s
20in2AS2 + -16in4sAS = 5S + -5s

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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