8x^2-13xy+5y^2=0

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


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

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

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

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(8x + -5y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8x + -5y)' equal to zero and attempt to solve:

Simplifying
8x + -5y = 0

Solving
8x + -5y = 0

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

Add '5y' to each side of the equation.
8x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
8x + 0 = 0 + 5y
8x = 0 + 5y
Remove the zero:
8x = 5y

Divide each side by '8'.
x = 0.625y

Simplifying
x = 0.625y
Solution
x = {y, 0.625y}

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