10x^2+21xy-10y^2=0

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Solution for 10x^2+21xy-10y^2=0 equation: 


Simplifying
10x2 + 21xy + -10y2 = 0

Reorder the terms:
21xy + 10x2 + -10y2 = 0

Solving
21xy + 10x2 + -10y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {0.4y, -2.5y}

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