6x(3x-2y)-3x(6y-x)+9xy=

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Solution for 6x(3x-2y)-3x(6y-x)+9xy= equation: 


Simplifying
6x(3x + -2y) + -3x(6y + -1x) + 9xy = 0
(3x * 6x + -2y * 6x) + -3x(6y + -1x) + 9xy = 0

Reorder the terms:
(-12xy + 18x2) + -3x(6y + -1x) + 9xy = 0
(-12xy + 18x2) + -3x(6y + -1x) + 9xy = 0

Reorder the terms:
-12xy + 18x2 + -3x(-1x + 6y) + 9xy = 0
-12xy + 18x2 + (-1x * -3x + 6y * -3x) + 9xy = 0

Reorder the terms:
-12xy + 18x2 + (-18xy + 3x2) + 9xy = 0
-12xy + 18x2 + (-18xy + 3x2) + 9xy = 0

Reorder the terms:
-12xy + -18xy + 9xy + 18x2 + 3x2 = 0

Combine like terms: -12xy + -18xy = -30xy
-30xy + 9xy + 18x2 + 3x2 = 0

Combine like terms: -30xy + 9xy = -21xy
-21xy + 18x2 + 3x2 = 0

Combine like terms: 18x2 + 3x2 = 21x2
-21xy + 21x2 = 0

Solving
-21xy + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '21x'.
21x(-1y + x) = 0

Ignore the factor 21.

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 '(-1y + x)' equal to zero and attempt to solve:

Simplifying
-1y + x = 0

Reorder the terms:
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
Solution
x = {0, y}

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