sin(6x)sin(4x)+sin(10x)=0

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Solution for sin(6x)sin(4x)+sin(10x)=0 equation: 


Simplifying
sin(6x) * sin(4x) + sin(10x) = 0

Remove parenthesis around (6x)
ins * 6x * sin(4x) + sin(10x) = 0

Remove parenthesis around (4x)
ins * 6x * ins * 4x + sin(10x) = 0

Reorder the terms for easier multiplication:
6 * 4ins * x * ins * x + sin(10x) = 0

Multiply 6 * 4
24ins * x * ins * x + sin(10x) = 0

Multiply ins * x
24insx * ins * x + sin(10x) = 0

Multiply insx * ins
24i2n2s2x * x + sin(10x) = 0

Multiply i2n2s2x * x
24i2n2s2x2 + sin(10x) = 0

Remove parenthesis around (10x)
24i2n2s2x2 + ins * 10x = 0

Reorder the terms for easier multiplication:
24i2n2s2x2 + 10ins * x = 0

Multiply ins * x
24i2n2s2x2 + 10insx = 0

Reorder the terms:
10insx + 24i2n2s2x2 = 0

Solving
10insx + 24i2n2s2x2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2insx'.
2insx(5 + 12insx) = 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 '(5 + 12insx)' equal to zero and attempt to solve:

Simplifying
5 + 12insx = 0

Solving
5 + 12insx = 0

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

Add '-5' to each side of the equation.
5 + -5 + 12insx = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 12insx = 0 + -5
12insx = 0 + -5

Combine like terms: 0 + -5 = -5
12insx = -5

Divide each side by '12nsx'.
i = -0.4166666667n-1s-1x-1

Simplifying
i = -0.4166666667n-1s-1x-1
Solution
i = {-0.4166666667n-1s-1x-1}

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