sin(2x)*sin(6x)*sin(4x)=0.25*sin(8x)

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Solution for sin(2x)*sin(6x)*sin(4x)=0.25*sin(8x) equation: 


Simplifying
sin(2x) * sin(6x) * sin(4x) = 0.25sin(8x)

Remove parenthesis around (2x)
ins * 2x * sin(6x) * sin(4x) = 0.25sin(8x)

Remove parenthesis around (6x)
ins * 2x * ins * 6x * sin(4x) = 0.25sin(8x)

Remove parenthesis around (4x)
ins * 2x * ins * 6x * ins * 4x = 0.25sin(8x)

Reorder the terms for easier multiplication:
2 * 6 * 4ins * x * ins * x * ins * x = 0.25sin(8x)

Multiply 2 * 6
12 * 4ins * x * ins * x * ins * x = 0.25sin(8x)

Multiply 12 * 4
48ins * x * ins * x * ins * x = 0.25sin(8x)

Multiply ins * x
48insx * ins * x * ins * x = 0.25sin(8x)

Multiply insx * ins
48i2n2s2x * x * ins * x = 0.25sin(8x)

Multiply i2n2s2x * x
48i2n2s2x2 * ins * x = 0.25sin(8x)

Multiply i2n2s2x2 * ins
48i3n3s3x2 * x = 0.25sin(8x)

Multiply i3n3s3x2 * x
48i3n3s3x3 = 0.25sin(8x)

Remove parenthesis around (8x)
48i3n3s3x3 = 0.25ins * 8x

Reorder the terms for easier multiplication:
48i3n3s3x3 = 0.25 * 8ins * x

Multiply 0.25 * 8
48i3n3s3x3 = 2ins * x

Multiply ins * x
48i3n3s3x3 = 2insx

Solving
48i3n3s3x3 = 2insx

Solving for variable 'i'.

Reorder the terms:
-2insx + 48i3n3s3x3 = 2insx + -2insx

Combine like terms: 2insx + -2insx = 0
-2insx + 48i3n3s3x3 = 0

Factor out the Greatest Common Factor (GCF), '2insx'.
2insx(-1 + 24i2n2s2x2) = 0

Ignore the factor 2.

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

Simplifying
insx = 0

Solving
insx = 0

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

Simplifying
insx = 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 '(-1 + 24i2n2s2x2)' equal to zero and attempt to solve:

Simplifying
-1 + 24i2n2s2x2 = 0

Solving
-1 + 24i2n2s2x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 24i2n2s2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 24i2n2s2x2 = 0 + 1
24i2n2s2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
24i2n2s2x2 = 1

Divide each side by '24n2s2x2'.
i2 = 0.04166666667n-2s-2x-2

Simplifying
i2 = 0.04166666667n-2s-2x-2

Take the square root of each side:
i = {-0.204124145n-1s-1x-1, 0.204124145n-1s-1x-1}
Solution
i = {-0.204124145n-1s-1x-1, 0.204124145n-1s-1x-1}

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