-y(2y+4x)(y-x)=

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


Simplifying
-1y(2y + 4x)(y + -1x) = 0

Reorder the terms:
-1y(4x + 2y)(y + -1x) = 0

Reorder the terms:
-1y(4x + 2y)(-1x + y) = 0

Multiply (4x + 2y) * (-1x + y)
-1y(4x * (-1x + y) + 2y * (-1x + y)) = 0
-1y((-1x * 4x + y * 4x) + 2y * (-1x + y)) = 0

Reorder the terms:
-1y((4xy + -4x2) + 2y * (-1x + y)) = 0
-1y((4xy + -4x2) + 2y * (-1x + y)) = 0
-1y(4xy + -4x2 + (-1x * 2y + y * 2y)) = 0
-1y(4xy + -4x2 + (-2xy + 2y2)) = 0

Reorder the terms:
-1y(4xy + -2xy + -4x2 + 2y2) = 0

Combine like terms: 4xy + -2xy = 2xy
-1y(2xy + -4x2 + 2y2) = 0
(2xy * -1y + -4x2 * -1y + 2y2 * -1y) = 0
(-2xy2 + 4x2y + -2y3) = 0

Solving
-2xy2 + 4x2y + -2y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-1xy + 2x2 + -1y2) = 0

Factor a trinomial.
2y((x + -1y)(2x + y)) = 0

Ignore the factor 2.

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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

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

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

Simplifying
x = -0.5y
Solution
x = {y, -0.5y}

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