4x^2-6xy+6x^2+3y^2+2a^2+3xy-x^2-3y^2-2a^2+9x^2=

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Solution for 4x^2-6xy+6x^2+3y^2+2a^2+3xy-x^2-3y^2-2a^2+9x^2= equation: 


Simplifying
4x2 + -6xy + 6x2 + 3y2 + 2a2 + 3xy + -1x2 + -3y2 + -2a2 + 9x2 = 0

Reorder the terms:
2a2 + -2a2 + -6xy + 3xy + 4x2 + 6x2 + -1x2 + 9x2 + 3y2 + -3y2 = 0

Combine like terms: 2a2 + -2a2 = 0
0 + -6xy + 3xy + 4x2 + 6x2 + -1x2 + 9x2 + 3y2 + -3y2 = 0
-6xy + 3xy + 4x2 + 6x2 + -1x2 + 9x2 + 3y2 + -3y2 = 0

Combine like terms: -6xy + 3xy = -3xy
-3xy + 4x2 + 6x2 + -1x2 + 9x2 + 3y2 + -3y2 = 0

Combine like terms: 4x2 + 6x2 = 10x2
-3xy + 10x2 + -1x2 + 9x2 + 3y2 + -3y2 = 0

Combine like terms: 10x2 + -1x2 = 9x2
-3xy + 9x2 + 9x2 + 3y2 + -3y2 = 0

Combine like terms: 9x2 + 9x2 = 18x2
-3xy + 18x2 + 3y2 + -3y2 = 0

Combine like terms: 3y2 + -3y2 = 0
-3xy + 18x2 + 0 = 0
-3xy + 18x2 = 0

Solving
-3xy + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1y + 6x) = 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 '(-1y + 6x)' equal to zero and attempt to solve:

Simplifying
-1y + 6x = 0

Reorder the terms:
6x + -1y = 0

Solving
6x + -1y = 0

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

Add 'y' to each side of the equation.
6x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
6x + 0 = 0 + y
6x = 0 + y
Remove the zero:
6x = y

Divide each side by '6'.
x = 0.1666666667y

Simplifying
x = 0.1666666667y
Solution
x = {0, 0.1666666667y}

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