5x^2-65xy-150y^2=0

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Solution for 5x^2-65xy-150y^2=0 equation: 


Simplifying
5x2 + -65xy + -150y2 = 0

Reorder the terms:
-65xy + 5x2 + -150y2 = 0

Solving
-65xy + 5x2 + -150y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-13xy + x2 + -30y2) = 0

Factor a trinomial.
5((x + -15y)(x + 2y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(x + -15y)' equal to zero and attempt to solve:

Simplifying
x + -15y = 0

Solving
x + -15y = 0

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

Add '15y' to each side of the equation.
x + -15y + 15y = 0 + 15y

Combine like terms: -15y + 15y = 0
x + 0 = 0 + 15y
x = 0 + 15y
Remove the zero:
x = 15y

Simplifying
x = 15y

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y
Solution
x = {15y, -2y}

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