2y^2-6xy-56x^2=0

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Solution for 2y^2-6xy-56x^2=0 equation: 


Simplifying
2y2 + -6xy + -56x2 = 0

Reorder the terms:
-6xy + -56x2 + 2y2 = 0

Solving
-6xy + -56x2 + 2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3xy + -28x2 + y2) = 0

Factor a trinomial.
2((-4x + -1y)(7x + -1y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4x + -1y)' equal to zero and attempt to solve:

Simplifying
-4x + -1y = 0

Solving
-4x + -1y = 0

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

Add 'y' to each side of the equation.
-4x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-4x + 0 = 0 + y
-4x = 0 + y
Remove the zero:
-4x = y

Divide each side by '-4'.
x = -0.25y

Simplifying
x = -0.25y

Subproblem 2
Set the factor '(7x + -1y)' equal to zero and attempt to solve:

Simplifying
7x + -1y = 0

Solving
7x + -1y = 0

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

Add 'y' to each side of the equation.
7x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
7x + 0 = 0 + y
7x = 0 + y
Remove the zero:
7x = y

Divide each side by '7'.
x = 0.1428571429y

Simplifying
x = 0.1428571429y
Solution
x = {-0.25y, 0.1428571429y}

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