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

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


Simplifying
4x2 + 9y2 = 12y * x

Multiply y * x
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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