17y^2-17x^2=32y^2-64xy+48x^2

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Solution for 17y^2-17x^2=32y^2-64xy+48x^2 equation: 


Simplifying
17y2 + -17x2 = 32y2 + -64xy + 48x2

Reorder the terms:
-17x2 + 17y2 = 32y2 + -64xy + 48x2

Reorder the terms:
-17x2 + 17y2 = -64xy + 48x2 + 32y2

Solving
-17x2 + 17y2 = -64xy + 48x2 + 32y2

Solving for variable 'x'.

Reorder the terms:
64xy + -17x2 + -48x2 + 17y2 + -32y2 = -64xy + 48x2 + 32y2 + 64xy + -48x2 + -32y2

Combine like terms: -17x2 + -48x2 = -65x2
64xy + -65x2 + 17y2 + -32y2 = -64xy + 48x2 + 32y2 + 64xy + -48x2 + -32y2

Combine like terms: 17y2 + -32y2 = -15y2
64xy + -65x2 + -15y2 = -64xy + 48x2 + 32y2 + 64xy + -48x2 + -32y2

Reorder the terms:
64xy + -65x2 + -15y2 = -64xy + 64xy + 48x2 + -48x2 + 32y2 + -32y2

Combine like terms: -64xy + 64xy = 0
64xy + -65x2 + -15y2 = 0 + 48x2 + -48x2 + 32y2 + -32y2
64xy + -65x2 + -15y2 = 48x2 + -48x2 + 32y2 + -32y2

Combine like terms: 48x2 + -48x2 = 0
64xy + -65x2 + -15y2 = 0 + 32y2 + -32y2
64xy + -65x2 + -15y2 = 32y2 + -32y2

Combine like terms: 32y2 + -32y2 = 0
64xy + -65x2 + -15y2 = 0

Factor a trinomial.
(-13x + 5y)(5x + -3y) = 0


Subproblem 1
Set the factor '(-13x + 5y)' equal to zero and attempt to solve:

Simplifying
-13x + 5y = 0

Solving
-13x + 5y = 0

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

Add '-5y' to each side of the equation.
-13x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
-13x + 0 = 0 + -5y
-13x = 0 + -5y
Remove the zero:
-13x = -5y

Divide each side by '-13'.
x = 0.3846153846y

Simplifying
x = 0.3846153846y

Subproblem 2
Set the factor '(5x + -3y)' equal to zero and attempt to solve:

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

Add '3y' to each side of the equation.
5x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
5x + 0 = 0 + 3y
5x = 0 + 3y
Remove the zero:
5x = 3y

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y
Solution
x = {0.3846153846y, 0.6y}

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