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

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


Simplifying
3x2 + -1xy + -4y2 = 0

Reorder the terms:
-1xy + 3x2 + -4y2 = 0

Solving
-1xy + 3x2 + -4y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -4y)(x + y) = 0


Subproblem 1
Set the factor '(3x + -4y)' equal to zero and attempt to solve:

Simplifying
3x + -4y = 0

Solving
3x + -4y = 0

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

Add '4y' to each side of the equation.
3x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
3x + 0 = 0 + 4y
3x = 0 + 4y
Remove the zero:
3x = 4y

Divide each side by '3'.
x = 1.333333333y

Simplifying
x = 1.333333333y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {1.333333333y, -1y}

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