x(3xy-y)-y(x^2-xy+x)=

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


Simplifying
x(3xy + -1y) + -1y(x2 + -1xy + x) = 0
(3xy * x + -1y * x) + -1y(x2 + -1xy + x) = 0

Reorder the terms:
(-1xy + 3x2y) + -1y(x2 + -1xy + x) = 0
(-1xy + 3x2y) + -1y(x2 + -1xy + x) = 0

Reorder the terms:
-1xy + 3x2y + -1y(x + -1xy + x2) = 0
-1xy + 3x2y + (x * -1y + -1xy * -1y + x2 * -1y) = 0
-1xy + 3x2y + (-1xy + 1xy2 + -1x2y) = 0

Reorder the terms:
-1xy + -1xy + 1xy2 + 3x2y + -1x2y = 0

Combine like terms: -1xy + -1xy = -2xy
-2xy + 1xy2 + 3x2y + -1x2y = 0

Combine like terms: 3x2y + -1x2y = 2x2y
-2xy + 1xy2 + 2x2y = 0

Solving
-2xy + 1xy2 + 2x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-2 + y + 2x) = 0


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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 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 '(-2 + y + 2x)' equal to zero and attempt to solve:

Simplifying
-2 + y + 2x = 0

Reorder the terms:
-2 + 2x + y = 0

Solving
-2 + 2x + y = 0

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

Add '2' to each side of the equation.
-2 + 2x + 2 + y = 0 + 2

Reorder the terms:
-2 + 2 + 2x + y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2x + y = 0 + 2
2x + y = 0 + 2

Combine like terms: 0 + 2 = 2
2x + y = 2

Add '-1y' to each side of the equation.
2x + y + -1y = 2 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 2 + -1y
2x = 2 + -1y

Divide each side by '2'.
x = 1 + -0.5y

Simplifying
x = 1 + -0.5y
Solution
x = {1 + -0.5y}

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