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

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


Simplifying
4x2 + 9y2 = 12xy

Solving
4x2 + 9y2 = 12xy

Solving for variable 'x'.

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

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

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

Subproblem 1

Set the factor '(2x + -3y)' equal to zero and attempt to solve: Simplifying 2x + -3y = 0 Solving 2x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 2x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 = 0 + 3y 2x = 0 + 3y Remove the zero: 2x = 3y Divide each side by '2'. x = 1.5y Simplifying x = 1.5y

Subproblem 2

Set the factor '(2x + -3y)' equal to zero and attempt to solve: Simplifying 2x + -3y = 0 Solving 2x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 2x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 = 0 + 3y 2x = 0 + 3y Remove the zero: 2x = 3y Divide each side by '2'. x = 1.5y Simplifying x = 1.5y

Solution

x = {1.5y, 1.5y}

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