4*y^2+9*x^2=12*x*y

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Solution for 4*y^2+9*x^2=12*x*y equation:


Simplifying
4y2 + 9x2 = 12x * y

Reorder the terms:
9x2 + 4y2 = 12x * y

Multiply x * y
9x2 + 4y2 = 12xy

Solving
9x2 + 4y2 = 12xy

Solving for variable 'x'.

Reorder the terms:
-12xy + 9x2 + 4y2 = 12xy + -12xy

Combine like terms: 12xy + -12xy = 0
-12xy + 9x2 + 4y2 = 0

Factor a trinomial.
(3x + -2y)(3x + -2y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3x + -2y)' equal to zero and attempt to solve: Simplifying 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 = {0.6666666667y, 0.6666666667y}

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