10x^2+3xy-y^2=0

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Solution for 10x^2+3xy-y^2=0 equation: 


Simplifying
10x2 + 3xy + -1y2 = 0

Reorder the terms:
3xy + 10x2 + -1y2 = 0

Solving
3xy + 10x2 + -1y2 = 0

Solving for variable 'x'.

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


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

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

Add 'y' to each side of the equation.
5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
5x + 0 = 0 + y
5x = 0 + y
Remove the zero:
5x = y

Divide each side by '5'.
x = 0.2y

Simplifying
x = 0.2y

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

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

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

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

Simplifying
x = -0.5y
Solution
x = {0.2y, -0.5y}

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