36x^2+24xy+4y^2=9x^2+54xy+81y^2

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Solution for 36x^2+24xy+4y^2=9x^2+54xy+81y^2 equation: 


Simplifying
36x2 + 24xy + 4y2 = 9x2 + 54xy + 81y2

Reorder the terms:
24xy + 36x2 + 4y2 = 9x2 + 54xy + 81y2

Reorder the terms:
24xy + 36x2 + 4y2 = 54xy + 9x2 + 81y2

Solving
24xy + 36x2 + 4y2 = 54xy + 9x2 + 81y2

Solving for variable 'x'.

Reorder the terms:
24xy + -54xy + 36x2 + -9x2 + 4y2 + -81y2 = 54xy + 9x2 + 81y2 + -54xy + -9x2 + -81y2

Combine like terms: 24xy + -54xy = -30xy
-30xy + 36x2 + -9x2 + 4y2 + -81y2 = 54xy + 9x2 + 81y2 + -54xy + -9x2 + -81y2

Combine like terms: 36x2 + -9x2 = 27x2
-30xy + 27x2 + 4y2 + -81y2 = 54xy + 9x2 + 81y2 + -54xy + -9x2 + -81y2

Combine like terms: 4y2 + -81y2 = -77y2
-30xy + 27x2 + -77y2 = 54xy + 9x2 + 81y2 + -54xy + -9x2 + -81y2

Reorder the terms:
-30xy + 27x2 + -77y2 = 54xy + -54xy + 9x2 + -9x2 + 81y2 + -81y2

Combine like terms: 54xy + -54xy = 0
-30xy + 27x2 + -77y2 = 0 + 9x2 + -9x2 + 81y2 + -81y2
-30xy + 27x2 + -77y2 = 9x2 + -9x2 + 81y2 + -81y2

Combine like terms: 9x2 + -9x2 = 0
-30xy + 27x2 + -77y2 = 0 + 81y2 + -81y2
-30xy + 27x2 + -77y2 = 81y2 + -81y2

Combine like terms: 81y2 + -81y2 = 0
-30xy + 27x2 + -77y2 = 0

Factor a trinomial.
(3x + -7y)(9x + 11y) = 0


Subproblem 1
Set the factor '(3x + -7y)' equal to zero and attempt to solve:

Simplifying
3x + -7y = 0

Solving
3x + -7y = 0

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

Add '7y' to each side of the equation.
3x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
3x + 0 = 0 + 7y
3x = 0 + 7y
Remove the zero:
3x = 7y

Divide each side by '3'.
x = 2.333333333y

Simplifying
x = 2.333333333y

Subproblem 2
Set the factor '(9x + 11y)' equal to zero and attempt to solve:

Simplifying
9x + 11y = 0

Solving
9x + 11y = 0

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

Add '-11y' to each side of the equation.
9x + 11y + -11y = 0 + -11y

Combine like terms: 11y + -11y = 0
9x + 0 = 0 + -11y
9x = 0 + -11y
Remove the zero:
9x = -11y

Divide each side by '9'.
x = -1.222222222y

Simplifying
x = -1.222222222y
Solution
x = {2.333333333y, -1.222222222y}

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