(6x^2y-10xy+3xy^2)-(10x^2y+5xy+2xy^2)=

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Solution for (6x^2y-10xy+3xy^2)-(10x^2y+5xy+2xy^2)= equation: 


Simplifying
(6x2y + -10xy + 3xy2) + -1(10x2y + 5xy + 2xy2) = 0

Reorder the terms:
(-10xy + 3xy2 + 6x2y) + -1(10x2y + 5xy + 2xy2) = 0

Remove parenthesis around (-10xy + 3xy2 + 6x2y)
-10xy + 3xy2 + 6x2y + -1(10x2y + 5xy + 2xy2) = 0

Reorder the terms:
-10xy + 3xy2 + 6x2y + -1(5xy + 2xy2 + 10x2y) = 0
-10xy + 3xy2 + 6x2y + (5xy * -1 + 2xy2 * -1 + 10x2y * -1) = 0
-10xy + 3xy2 + 6x2y + (-5xy + -2xy2 + -10x2y) = 0

Reorder the terms:
-10xy + -5xy + 3xy2 + -2xy2 + 6x2y + -10x2y = 0

Combine like terms: -10xy + -5xy = -15xy
-15xy + 3xy2 + -2xy2 + 6x2y + -10x2y = 0

Combine like terms: 3xy2 + -2xy2 = 1xy2
-15xy + 1xy2 + 6x2y + -10x2y = 0

Combine like terms: 6x2y + -10x2y = -4x2y
-15xy + 1xy2 + -4x2y = 0

Solving
-15xy + 1xy2 + -4x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-15 + y + -4x) = 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 '(-15 + y + -4x)' equal to zero and attempt to solve:

Simplifying
-15 + y + -4x = 0

Reorder the terms:
-15 + -4x + y = 0

Solving
-15 + -4x + y = 0

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

Add '15' to each side of the equation.
-15 + -4x + 15 + y = 0 + 15

Reorder the terms:
-15 + 15 + -4x + y = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4x + y = 0 + 15
-4x + y = 0 + 15

Combine like terms: 0 + 15 = 15
-4x + y = 15

Add '-1y' to each side of the equation.
-4x + y + -1y = 15 + -1y

Combine like terms: y + -1y = 0
-4x + 0 = 15 + -1y
-4x = 15 + -1y

Divide each side by '-4'.
x = -3.75 + 0.25y

Simplifying
x = -3.75 + 0.25y
Solution
x = {-3.75 + 0.25y}

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