10x^2-23xy+9y^2=0

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Solution for 10x^2-23xy+9y^2=0 equation: 


Simplifying
10x2 + -23xy + 9y2 = 0

Reorder the terms:
-23xy + 10x2 + 9y2 = 0

Solving
-23xy + 10x2 + 9y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -9y)(2x + -1y) = 0


Subproblem 1
Set the factor '(5x + -9y)' equal to zero and attempt to solve:

Simplifying
5x + -9y = 0

Solving
5x + -9y = 0

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

Add '9y' to each side of the equation.
5x + -9y + 9y = 0 + 9y

Combine like terms: -9y + 9y = 0
5x + 0 = 0 + 9y
5x = 0 + 9y
Remove the zero:
5x = 9y

Divide each side by '5'.
x = 1.8y

Simplifying
x = 1.8y

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 = {1.8y, 0.5y}

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