0=K(sinh(x+2y)+3sin(3x+y)-5x-y)

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Solution for 0=K(sinh(x+2y)+3sin(3x+y)-5x-y) equation:


Simplifying
0 = K(sinh(x + 2y) + 3sin(3x + y) + -5x + -1y)
0 = K((x * hins + 2y * hins) + 3sin(3x + y) + -5x + -1y)
0 = K((hinsx + 2hinsy) + 3sin(3x + y) + -5x + -1y)
0 = K(hinsx + 2hinsy + (3x * 3ins + y * 3ins) + -5x + -1y)
0 = K(hinsx + 2hinsy + (9insx + 3insy) + -5x + -1y)
0 = (hinsx * K + 2hinsy * K + 9insx * K + 3insy * K + -5x * K + -1y * K)
0 = (hinsxK + 2hinsyK + 9insxK + 3insyK + -5xK + -1yK)

Solving
0 = hinsxK + 2hinsyK + 9insxK + 3insyK + -5xK + -1yK

Solving for variable 'h'.

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

Add '-1hinsxK' to each side of the equation.
0 + -1hinsxK = hinsxK + 2hinsyK + 9insxK + 3insyK + -5xK + -1hinsxK + -1yK
Remove the zero:
-1hinsxK = hinsxK + 2hinsyK + 9insxK + 3insyK + -5xK + -1hinsxK + -1yK

Reorder the terms:
-1hinsxK = hinsxK + -1hinsxK + 2hinsyK + 9insxK + 3insyK + -5xK + -1yK

Combine like terms: hinsxK + -1hinsxK = 0
-1hinsxK = 0 + 2hinsyK + 9insxK + 3insyK + -5xK + -1yK
-1hinsxK = 2hinsyK + 9insxK + 3insyK + -5xK + -1yK

Add '-2hinsyK' to each side of the equation.
-1hinsxK + -2hinsyK = 2hinsyK + 9insxK + 3insyK + -5xK + -2hinsyK + -1yK

Reorder the terms:
-1hinsxK + -2hinsyK = 2hinsyK + -2hinsyK + 9insxK + 3insyK + -5xK + -1yK

Combine like terms: 2hinsyK + -2hinsyK = 0
-1hinsxK + -2hinsyK = 0 + 9insxK + 3insyK + -5xK + -1yK
-1hinsxK + -2hinsyK = 9insxK + 3insyK + -5xK + -1yK

Reorder the terms:
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = 9insxK + -9insxK + 3insyK + -3insyK + -5xK + 5xK + -1yK + yK

Combine like terms: 9insxK + -9insxK = 0
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = 0 + 3insyK + -3insyK + -5xK + 5xK + -1yK + yK
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = 3insyK + -3insyK + -5xK + 5xK + -1yK + yK

Combine like terms: 3insyK + -3insyK = 0
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = 0 + -5xK + 5xK + -1yK + yK
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = -5xK + 5xK + -1yK + yK

Combine like terms: -5xK + 5xK = 0
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = 0 + -1yK + yK
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = -1yK + yK

Combine like terms: -1yK + yK = 0
-1hinsxK + -2hinsyK + -9insxK + -3insyK + 5xK + yK = 0

Factor out the Greatest Common Factor (GCF), 'K'.
K(-1hinsx + -2hinsy + -9insx + -3insy + 5x + y) = 0

Subproblem 1

Set the factor 'K' equal to zero and attempt to solve: Simplifying K = 0 Solving K = 0 Move all terms containing h to the left, all other terms to the right. Add '-1K' to each side of the equation. K + -1K = 0 + -1K Remove the zero: 0 = -1K Simplifying 0 = -1K 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 '(-1hinsx + -2hinsy + -9insx + -3insy + 5x + y)' equal to zero and attempt to solve: Simplifying -1hinsx + -2hinsy + -9insx + -3insy + 5x + y = 0 Solving -1hinsx + -2hinsy + -9insx + -3insy + 5x + y = 0 Move all terms containing h to the left, all other terms to the right. Add '9insx' to each side of the equation. -1hinsx + -2hinsy + -9insx + -3insy + 5x + 9insx + y = 0 + 9insx Reorder the terms: -1hinsx + -2hinsy + -9insx + 9insx + -3insy + 5x + y = 0 + 9insx Combine like terms: -9insx + 9insx = 0 -1hinsx + -2hinsy + 0 + -3insy + 5x + y = 0 + 9insx -1hinsx + -2hinsy + -3insy + 5x + y = 0 + 9insx Remove the zero: -1hinsx + -2hinsy + -3insy + 5x + y = 9insx Add '3insy' to each side of the equation. -1hinsx + -2hinsy + -3insy + 5x + 3insy + y = 9insx + 3insy Reorder the terms: -1hinsx + -2hinsy + -3insy + 3insy + 5x + y = 9insx + 3insy Combine like terms: -3insy + 3insy = 0 -1hinsx + -2hinsy + 0 + 5x + y = 9insx + 3insy -1hinsx + -2hinsy + 5x + y = 9insx + 3insy Add '-5x' to each side of the equation. -1hinsx + -2hinsy + 5x + -5x + y = 9insx + 3insy + -5x Combine like terms: 5x + -5x = 0 -1hinsx + -2hinsy + 0 + y = 9insx + 3insy + -5x -1hinsx + -2hinsy + y = 9insx + 3insy + -5x Add '-1y' to each side of the equation. -1hinsx + -2hinsy + y + -1y = 9insx + 3insy + -5x + -1y Combine like terms: y + -1y = 0 -1hinsx + -2hinsy + 0 = 9insx + 3insy + -5x + -1y -1hinsx + -2hinsy = 9insx + 3insy + -5x + -1y 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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