5y^2-6xy-8x^2=0

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Solution for 5y^2-6xy-8x^2=0 equation: 


Simplifying
5y2 + -6xy + -8x2 = 0

Reorder the terms:
-6xy + -8x2 + 5y2 = 0

Solving
-6xy + -8x2 + 5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4x + -5y)(2x + -1y) = 0


Subproblem 1
Set the factor '(-4x + -5y)' equal to zero and attempt to solve:

Simplifying
-4x + -5y = 0

Solving
-4x + -5y = 0

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

Add '5y' to each side of the equation.
-4x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-4x + 0 = 0 + 5y
-4x = 0 + 5y
Remove the zero:
-4x = 5y

Divide each side by '-4'.
x = -1.25y

Simplifying
x = -1.25y

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

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

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

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

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {-1.25y, 0.5y}

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