10x^2-17xy-20y^2=0

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Solution for 10x^2-17xy-20y^2=0 equation: 


Simplifying
10x2 + -17xy + -20y2 = 0

Reorder the terms:
-17xy + 10x2 + -20y2 = 0

Solving
-17xy + 10x2 + -20y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y

Subproblem 2
Set the factor '(5x + 4y)' equal to zero and attempt to solve:

Simplifying
5x + 4y = 0

Solving
5x + 4y = 0

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

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

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

Divide each side by '5'.
x = -0.8y

Simplifying
x = -0.8y
Solution
x = {2.5y, -0.8y}

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