3x^2-23xy+40y^2=0

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Solution for 3x^2-23xy+40y^2=0 equation: 


Simplifying
3x2 + -23xy + 40y2 = 0

Reorder the terms:
-23xy + 3x2 + 40y2 = 0

Solving
-23xy + 3x2 + 40y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -5y)(3x + -8y) = 0


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

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

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

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

Simplifying
x = 5y

Subproblem 2
Set the factor '(3x + -8y)' equal to zero and attempt to solve:

Simplifying
3x + -8y = 0

Solving
3x + -8y = 0

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

Add '8y' to each side of the equation.
3x + -8y + 8y = 0 + 8y

Combine like terms: -8y + 8y = 0
3x + 0 = 0 + 8y
3x = 0 + 8y
Remove the zero:
3x = 8y

Divide each side by '3'.
x = 2.666666667y

Simplifying
x = 2.666666667y
Solution
x = {5y, 2.666666667y}

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