13y^2-5yx-8x^2=0

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Solution for 13y^2-5yx-8x^2=0 equation: 


Simplifying
13y2 + -5yx + -8x2 = 0

Reorder the terms:
-5xy + -8x2 + 13y2 = 0

Solving
-5xy + -8x2 + 13y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8x + -13y)(x + -1y) = 0


Subproblem 1
Set the factor '(-8x + -13y)' equal to zero and attempt to solve:

Simplifying
-8x + -13y = 0

Solving
-8x + -13y = 0

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

Add '13y' to each side of the equation.
-8x + -13y + 13y = 0 + 13y

Combine like terms: -13y + 13y = 0
-8x + 0 = 0 + 13y
-8x = 0 + 13y
Remove the zero:
-8x = 13y

Divide each side by '-8'.
x = -1.625y

Simplifying
x = -1.625y

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y
Solution
x = {-1.625y, y}

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