7x^2-5xy-2y^2=0

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Solution for 7x^2-5xy-2y^2=0 equation: 


Simplifying
7x2 + -5xy + -2y2 = 0

Reorder the terms:
-5xy + 7x2 + -2y2 = 0

Solving
-5xy + 7x2 + -2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(7x + 2y) = 0


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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y

Subproblem 2
Set the factor '(7x + 2y)' equal to zero and attempt to solve:

Simplifying
7x + 2y = 0

Solving
7x + 2y = 0

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

Add '-2y' to each side of the equation.
7x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
7x + 0 = 0 + -2y
7x = 0 + -2y
Remove the zero:
7x = -2y

Divide each side by '7'.
x = -0.2857142857y

Simplifying
x = -0.2857142857y
Solution
x = {y, -0.2857142857y}

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