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

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


Simplifying
0 = (2x + -3y)(4x2 + -2xy + 2xy2)

Reorder the terms:
0 = (2x + -3y)(-2xy + 2xy2 + 4x2)

Multiply (2x + -3y) * (-2xy + 2xy2 + 4x2)
0 = (2x * (-2xy + 2xy2 + 4x2) + -3y * (-2xy + 2xy2 + 4x2))
0 = ((-2xy * 2x + 2xy2 * 2x + 4x2 * 2x) + -3y * (-2xy + 2xy2 + 4x2))
0 = ((-4x2y + 4x2y2 + 8x3) + -3y * (-2xy + 2xy2 + 4x2))
0 = (-4x2y + 4x2y2 + 8x3 + (-2xy * -3y + 2xy2 * -3y + 4x2 * -3y))
0 = (-4x2y + 4x2y2 + 8x3 + (6xy2 + -6xy3 + -12x2y))

Reorder the terms:
0 = (6xy2 + -6xy3 + -4x2y + -12x2y + 4x2y2 + 8x3)

Combine like terms: -4x2y + -12x2y = -16x2y
0 = (6xy2 + -6xy3 + -16x2y + 4x2y2 + 8x3)

Solving
0 = 6xy2 + -6xy3 + -16x2y + 4x2y2 + 8x3

Solving for variable 'x'.
Remove the zero:
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 6xy2 + -6xy3 + -16x2y + 4x2y2 + 8x3 + -6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3

Reorder the terms:
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 6xy2 + -6xy2 + -6xy3 + 6xy3 + -16x2y + 16x2y + 4x2y2 + -4x2y2 + 8x3 + -8x3

Combine like terms: 6xy2 + -6xy2 = 0
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 0 + -6xy3 + 6xy3 + -16x2y + 16x2y + 4x2y2 + -4x2y2 + 8x3 + -8x3
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = -6xy3 + 6xy3 + -16x2y + 16x2y + 4x2y2 + -4x2y2 + 8x3 + -8x3

Combine like terms: -6xy3 + 6xy3 = 0
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 0 + -16x2y + 16x2y + 4x2y2 + -4x2y2 + 8x3 + -8x3
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = -16x2y + 16x2y + 4x2y2 + -4x2y2 + 8x3 + -8x3

Combine like terms: -16x2y + 16x2y = 0
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 0 + 4x2y2 + -4x2y2 + 8x3 + -8x3
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 4x2y2 + -4x2y2 + 8x3 + -8x3

Combine like terms: 4x2y2 + -4x2y2 = 0
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 0 + 8x3 + -8x3
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 8x3 + -8x3

Combine like terms: 8x3 + -8x3 = 0
-6xy2 + 6xy3 + 16x2y + -4x2y2 + -8x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3y2 + 3y3 + 8xy + -2xy2 + -4x2) = 0

Ignore the factor 2.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-3y2 + 3y3 + 8xy + -2xy2 + -4x2)' equal to zero and attempt to solve:

Simplifying
-3y2 + 3y3 + 8xy + -2xy2 + -4x2 = 0

Reorder the terms:
8xy + -2xy2 + -4x2 + -3y2 + 3y3 = 0

Solving
8xy + -2xy2 + -4x2 + -3y2 + 3y3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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