3sinx=-4sin(x-3)

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Solution for 3sinx=-4sin(x-3) equation: 


Simplifying
3sinx = -4sin(x + -3)

Reorder the terms:
3insx = -4ins(-3 + x)
3insx = (-3 * -4ins + x * -4ins)
3insx = (12ins + -4insx)

Solving
3insx = 12ins + -4insx

Solving for variable 'i'.

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

Add '-12ins' to each side of the equation.
-12ins + 3insx = 12ins + -12ins + -4insx

Combine like terms: 12ins + -12ins = 0
-12ins + 3insx = 0 + -4insx
-12ins + 3insx = -4insx

Add '4insx' to each side of the equation.
-12ins + 3insx + 4insx = -4insx + 4insx

Combine like terms: 3insx + 4insx = 7insx
-12ins + 7insx = -4insx + 4insx

Combine like terms: -4insx + 4insx = 0
-12ins + 7insx = 0

Factor out the Greatest Common Factor (GCF), 'ins'.
ins(-12 + 7x) = 0


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

Simplifying
ins = 0

Solving
ins = 0

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

Simplifying
ins = 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 '(-12 + 7x)' equal to zero and attempt to solve:

Simplifying
-12 + 7x = 0

Solving
-12 + 7x = 0

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

Add '12' to each side of the equation.
-12 + 12 + 7x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 7x = 0 + 12
7x = 0 + 12

Combine like terms: 0 + 12 = 12
7x = 12

Add '-7x' to each side of the equation.
7x + -7x = 12 + -7x

Combine like terms: 7x + -7x = 0
0 = 12 + -7x

Simplifying
0 = 12 + -7x

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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