y(z)(1+2z^1-1z^3)=x(z)(2z^1+1)

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Solution for y(z)(1+2z^1-1z^3)=x(z)(2z^1+1) equation:


Simplifying
y(z)(1 + 2z + -1z3) = x(z)(2z + 1)

Multiply y * z
yz(1 + 2z + -1z3) = x(z)(2z + 1)
(1 * yz + 2z * yz + -1z3 * yz) = x(z)(2z + 1)
(1yz + 2yz2 + -1yz4) = x(z)(2z + 1)

Reorder the terms:
1yz + 2yz2 + -1yz4 = x * z(1 + 2z)

Multiply x * z
1yz + 2yz2 + -1yz4 = xz(1 + 2z)
1yz + 2yz2 + -1yz4 = (1 * xz + 2z * xz)
1yz + 2yz2 + -1yz4 = (1xz + 2xz2)

Solving
1yz + 2yz2 + -1yz4 = 1xz + 2xz2

Solving for variable 'y'.

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

Reorder the terms:
-1xz + -2xz2 + 1yz + 2yz2 + -1yz4 = 1xz + 2xz2 + -1xz + -2xz2

Reorder the terms:
-1xz + -2xz2 + 1yz + 2yz2 + -1yz4 = 1xz + -1xz + 2xz2 + -2xz2

Combine like terms: 1xz + -1xz = 0
-1xz + -2xz2 + 1yz + 2yz2 + -1yz4 = 0 + 2xz2 + -2xz2
-1xz + -2xz2 + 1yz + 2yz2 + -1yz4 = 2xz2 + -2xz2

Combine like terms: 2xz2 + -2xz2 = 0
-1xz + -2xz2 + 1yz + 2yz2 + -1yz4 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-1x + -2xz + y + 2yz + -1yz3) = 0

Subproblem 1

Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing y to the left, all other terms to the right. Add '-1z' to each side of the equation. z + -1z = 0 + -1z Remove the zero: 0 = -1z Simplifying 0 = -1z 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 '(-1x + -2xz + y + 2yz + -1yz3)' equal to zero and attempt to solve: Simplifying -1x + -2xz + y + 2yz + -1yz3 = 0 Solving -1x + -2xz + y + 2yz + -1yz3 = 0 Move all terms containing y to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -2xz + y + 2yz + x + -1yz3 = 0 + x Reorder the terms: -1x + x + -2xz + y + 2yz + -1yz3 = 0 + x Combine like terms: -1x + x = 0 0 + -2xz + y + 2yz + -1yz3 = 0 + x -2xz + y + 2yz + -1yz3 = 0 + x Remove the zero: -2xz + y + 2yz + -1yz3 = x Add '2xz' to each side of the equation. -2xz + y + 2yz + 2xz + -1yz3 = x + 2xz Reorder the terms: -2xz + 2xz + y + 2yz + -1yz3 = x + 2xz Combine like terms: -2xz + 2xz = 0 0 + y + 2yz + -1yz3 = x + 2xz y + 2yz + -1yz3 = x + 2xz 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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