45x^2-177xy-12y^2=0

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Solution for 45x^2-177xy-12y^2=0 equation: 


Simplifying
45x2 + -177xy + -12y2 = 0

Reorder the terms:
-177xy + 45x2 + -12y2 = 0

Solving
-177xy + 45x2 + -12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-59xy + 15x2 + -4y2) = 0

Factor a trinomial.
3((x + -4y)(15x + y)) = 0

Ignore the factor 3.

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

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

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

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

Simplifying
x = 4y

Subproblem 2
Set the factor '(15x + y)' equal to zero and attempt to solve:

Simplifying
15x + y = 0

Solving
15x + y = 0

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

Add '-1y' to each side of the equation.
15x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
15x + 0 = 0 + -1y
15x = 0 + -1y
Remove the zero:
15x = -1y

Divide each side by '15'.
x = -0.06666666667y

Simplifying
x = -0.06666666667y
Solution
x = {4y, -0.06666666667y}

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