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

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


Simplifying
5x(3x + -6y) + -6x(6y + -1x) + 3xy = 0
(3x * 5x + -6y * 5x) + -6x(6y + -1x) + 3xy = 0

Reorder the terms:
(-30xy + 15x2) + -6x(6y + -1x) + 3xy = 0
(-30xy + 15x2) + -6x(6y + -1x) + 3xy = 0

Reorder the terms:
-30xy + 15x2 + -6x(-1x + 6y) + 3xy = 0
-30xy + 15x2 + (-1x * -6x + 6y * -6x) + 3xy = 0

Reorder the terms:
-30xy + 15x2 + (-36xy + 6x2) + 3xy = 0
-30xy + 15x2 + (-36xy + 6x2) + 3xy = 0

Reorder the terms:
-30xy + -36xy + 3xy + 15x2 + 6x2 = 0

Combine like terms: -30xy + -36xy = -66xy
-66xy + 3xy + 15x2 + 6x2 = 0

Combine like terms: -66xy + 3xy = -63xy
-63xy + 15x2 + 6x2 = 0

Combine like terms: 15x2 + 6x2 = 21x2
-63xy + 21x2 = 0

Solving
-63xy + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '21x'.
21x(-3y + 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 '(-3y + x)' equal to zero and attempt to solve:

Simplifying
-3y + x = 0

Reorder the terms:
x + -3y = 0

Solving
x + -3y = 0

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

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

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

Simplifying
x = 3y
Solution
x = {0, 3y}

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