sin(3x)=-sin^3(x)+3cos^2(x)sin(x)

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Solution for sin(3x)=-sin^3(x)+3cos^2(x)sin(x) equation: 


Simplifying
sin(3x) = -1sin3(x) + 3cos2(x) * sin(x)

Remove parenthesis around (3x)
ins * 3x = -1sin3(x) + 3cos2(x) * sin(x)

Reorder the terms for easier multiplication:
3ins * x = -1sin3(x) + 3cos2(x) * sin(x)

Multiply ins * x
3insx = -1sin3(x) + 3cos2(x) * sin(x)

Multiply in3s * x
3insx = -1in3sx + 3cos2(x) * sin(x)

Multiply cos2 * x
3insx = -1in3sx + 3cos2x * ins * x

Multiply cos2x * ins
3insx = -1in3sx + 3cinos3x * x

Multiply cinos3x * x
3insx = -1in3sx + 3cinos3x2

Reorder the terms:
3insx = 3cinos3x2 + -1in3sx

Solving
3insx = 3cinos3x2 + -1in3sx

Solving for variable 'i'.

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

Add '-3cinos3x2' to each side of the equation.
-3cinos3x2 + 3insx = 3cinos3x2 + -3cinos3x2 + -1in3sx

Combine like terms: 3cinos3x2 + -3cinos3x2 = 0
-3cinos3x2 + 3insx = 0 + -1in3sx
-3cinos3x2 + 3insx = -1in3sx

Add 'in3sx' to each side of the equation.
-3cinos3x2 + 3insx + in3sx = -1in3sx + in3sx

Combine like terms: -1in3sx + in3sx = 0
-3cinos3x2 + 3insx + in3sx = 0

Factor out the Greatest Common Factor (GCF), 'insx'.
insx(-3cos2x + 3 + n2) = 0


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 '(-3cos2x + 3 + n2)' equal to zero and attempt to solve:

Simplifying
-3cos2x + 3 + n2 = 0

Reorder the terms:
3 + -3cos2x + n2 = 0

Solving
3 + -3cos2x + n2 = 0

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

Add '-3' to each side of the equation.
3 + -3cos2x + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + -3cos2x + n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -3cos2x + n2 = 0 + -3
-3cos2x + n2 = 0 + -3

Combine like terms: 0 + -3 = -3
-3cos2x + n2 = -3

Add '3cos2x' to each side of the equation.
-3cos2x + 3cos2x + n2 = -3 + 3cos2x

Combine like terms: -3cos2x + 3cos2x = 0
0 + n2 = -3 + 3cos2x
n2 = -3 + 3cos2x

Add '-1n2' to each side of the equation.
n2 + -1n2 = -3 + 3cos2x + -1n2

Combine like terms: n2 + -1n2 = 0
0 = -3 + 3cos2x + -1n2

Simplifying
0 = -3 + 3cos2x + -1n2

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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