3x^2-xy-52y^2=0

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Solution for 3x^2-xy-52y^2=0 equation: 


Simplifying
3x2 + -1xy + -52y2 = 0

Reorder the terms:
-1xy + 3x2 + -52y2 = 0

Solving
-1xy + 3x2 + -52y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -13y)(x + 4y) = 0


Subproblem 1
Set the factor '(3x + -13y)' equal to zero and attempt to solve:

Simplifying
3x + -13y = 0

Solving
3x + -13y = 0

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

Add '13y' to each side of the equation.
3x + -13y + 13y = 0 + 13y

Combine like terms: -13y + 13y = 0
3x + 0 = 0 + 13y
3x = 0 + 13y
Remove the zero:
3x = 13y

Divide each side by '3'.
x = 4.333333333y

Simplifying
x = 4.333333333y

Subproblem 2
Set the factor '(x + 4y)' equal to zero and attempt to solve:

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

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

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

Simplifying
x = -4y
Solution
x = {4.333333333y, -4y}

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