4y^2-4xy-3x^2=0

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Solution for 4y^2-4xy-3x^2=0 equation: 


Simplifying
4y2 + -4xy + -3x2 = 0

Reorder the terms:
-4xy + -3x2 + 4y2 = 0

Solving
-4xy + -3x2 + 4y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1x + -2y)(3x + -2y) = 0


Subproblem 1
Set the factor '(-1x + -2y)' equal to zero and attempt to solve:

Simplifying
-1x + -2y = 0

Solving
-1x + -2y = 0

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

Add '2y' to each side of the equation.
-1x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
-1x + 0 = 0 + 2y
-1x = 0 + 2y
Remove the zero:
-1x = 2y

Divide each side by '-1'.
x = -2y

Simplifying
x = -2y

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 = {-2y, 0.6666666667y}

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