2x(3x-2y)-6x(2y-x)+8xy=

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Solution for 2x(3x-2y)-6x(2y-x)+8xy= equation: 


Simplifying
2x(3x + -2y) + -6x(2y + -1x) + 8xy = 0
(3x * 2x + -2y * 2x) + -6x(2y + -1x) + 8xy = 0

Reorder the terms:
(-4xy + 6x2) + -6x(2y + -1x) + 8xy = 0
(-4xy + 6x2) + -6x(2y + -1x) + 8xy = 0

Reorder the terms:
-4xy + 6x2 + -6x(-1x + 2y) + 8xy = 0
-4xy + 6x2 + (-1x * -6x + 2y * -6x) + 8xy = 0

Reorder the terms:
-4xy + 6x2 + (-12xy + 6x2) + 8xy = 0
-4xy + 6x2 + (-12xy + 6x2) + 8xy = 0

Reorder the terms:
-4xy + -12xy + 8xy + 6x2 + 6x2 = 0

Combine like terms: -4xy + -12xy = -16xy
-16xy + 8xy + 6x2 + 6x2 = 0

Combine like terms: -16xy + 8xy = -8xy
-8xy + 6x2 + 6x2 = 0

Combine like terms: 6x2 + 6x2 = 12x2
-8xy + 12x2 = 0

Solving
-8xy + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-2y + 3x) = 0

Ignore the factor 4.

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 '(-2y + 3x)' equal to zero and attempt to solve:

Simplifying
-2y + 3x = 0

Reorder the terms:
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y
Solution
x = {0, 0.6666666667y}

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