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

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


Simplifying
(2x2 + -5xy + 2y2)(3x2 + -6xy) = 0

Reorder the terms:
(-5xy + 2x2 + 2y2)(3x2 + -6xy) = 0

Reorder the terms:
(-5xy + 2x2 + 2y2)(-6xy + 3x2) = 0

Multiply (-5xy + 2x2 + 2y2) * (-6xy + 3x2)
(-5xy * (-6xy + 3x2) + 2x2 * (-6xy + 3x2) + 2y2 * (-6xy + 3x2)) = 0
((-6xy * -5xy + 3x2 * -5xy) + 2x2 * (-6xy + 3x2) + 2y2 * (-6xy + 3x2)) = 0
((30x2y2 + -15x3y) + 2x2 * (-6xy + 3x2) + 2y2 * (-6xy + 3x2)) = 0
(30x2y2 + -15x3y + (-6xy * 2x2 + 3x2 * 2x2) + 2y2 * (-6xy + 3x2)) = 0
(30x2y2 + -15x3y + (-12x3y + 6x4) + 2y2 * (-6xy + 3x2)) = 0
(30x2y2 + -15x3y + -12x3y + 6x4 + (-6xy * 2y2 + 3x2 * 2y2)) = 0
(30x2y2 + -15x3y + -12x3y + 6x4 + (-12xy3 + 6x2y2)) = 0

Reorder the terms:
(-12xy3 + 30x2y2 + 6x2y2 + -15x3y + -12x3y + 6x4) = 0

Combine like terms: 30x2y2 + 6x2y2 = 36x2y2
(-12xy3 + 36x2y2 + -15x3y + -12x3y + 6x4) = 0

Combine like terms: -15x3y + -12x3y = -27x3y
(-12xy3 + 36x2y2 + -27x3y + 6x4) = 0

Solving
-12xy3 + 36x2y2 + -27x3y + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4y3 + 12xy2 + -9x2y + 2x3) = 0

Ignore the factor 3.

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 '(-4y3 + 12xy2 + -9x2y + 2x3)' equal to zero and attempt to solve:

Simplifying
-4y3 + 12xy2 + -9x2y + 2x3 = 0

Reorder the terms:
12xy2 + -9x2y + 2x3 + -4y3 = 0

Solving
12xy2 + -9x2y + 2x3 + -4y3 = 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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