(x-y)(4x+xy-3y)+xy^2-x^2y=

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Solution for (x-y)(4x+xy-3y)+xy^2-x^2y= equation: 


Simplifying
(x + -1y)(4x + xy + -3y) + xy2 + -1x2y = 0

Multiply (x + -1y) * (4x + xy + -3y)
(x(4x + xy + -3y) + -1y * (4x + xy + -3y)) + xy2 + -1x2y = 0
((4x * x + xy * x + -3y * x) + -1y * (4x + xy + -3y)) + xy2 + -1x2y = 0

Reorder the terms:
((-3xy + 4x2 + x2y) + -1y * (4x + xy + -3y)) + xy2 + -1x2y = 0
((-3xy + 4x2 + x2y) + -1y * (4x + xy + -3y)) + xy2 + -1x2y = 0
(-3xy + 4x2 + x2y + (4x * -1y + xy * -1y + -3y * -1y)) + xy2 + -1x2y = 0
(-3xy + 4x2 + x2y + (-4xy + -1xy2 + 3y2)) + xy2 + -1x2y = 0

Reorder the terms:
(-3xy + -4xy + -1xy2 + 4x2 + x2y + 3y2) + xy2 + -1x2y = 0

Combine like terms: -3xy + -4xy = -7xy
(-7xy + -1xy2 + 4x2 + x2y + 3y2) + xy2 + -1x2y = 0

Reorder the terms:
-7xy + -1xy2 + xy2 + 4x2 + x2y + -1x2y + 3y2 = 0

Combine like terms: -1xy2 + xy2 = 0
-7xy + 0 + 4x2 + x2y + -1x2y + 3y2 = 0
-7xy + 4x2 + x2y + -1x2y + 3y2 = 0

Combine like terms: x2y + -1x2y = 0
-7xy + 4x2 + 0 + 3y2 = 0
-7xy + 4x2 + 3y2 = 0

Solving
-7xy + 4x2 + 3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(4x + -3y) = 0


Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y

Subproblem 2
Set the factor '(4x + -3y)' equal to zero and attempt to solve:

Simplifying
4x + -3y = 0

Solving
4x + -3y = 0

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

Add '3y' to each side of the equation.
4x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
4x + 0 = 0 + 3y
4x = 0 + 3y
Remove the zero:
4x = 3y

Divide each side by '4'.
x = 0.75y

Simplifying
x = 0.75y
Solution
x = {y, 0.75y}

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