5x^2-23xy-10y^2=0

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Solution for 5x^2-23xy-10y^2=0 equation: 


Simplifying
5x2 + -23xy + -10y2 = 0

Reorder the terms:
-23xy + 5x2 + -10y2 = 0

Solving
-23xy + 5x2 + -10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -5y)(5x + 2y) = 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 '(5x + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 2y = 0

Solving
5x + 2y = 0

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

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

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

Divide each side by '5'.
x = -0.4y

Simplifying
x = -0.4y
Solution
x = {5y, -0.4y}

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