6X^2-47XY+15Y^2=0

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Solution for 6X^2-47XY+15Y^2=0 equation: 


Simplifying
6X2 + -47XY + 15Y2 = 0

Reorder the terms:
-47XY + 6X2 + 15Y2 = 0

Solving
-47XY + 6X2 + 15Y2 = 0

Solving for variable 'X'.

Factor a trinomial.
(2X + -15Y)(3X + -1Y) = 0


Subproblem 1
Set the factor '(2X + -15Y)' equal to zero and attempt to solve:

Simplifying
2X + -15Y = 0

Solving
2X + -15Y = 0

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

Add '15Y' to each side of the equation.
2X + -15Y + 15Y = 0 + 15Y

Combine like terms: -15Y + 15Y = 0
2X + 0 = 0 + 15Y
2X = 0 + 15Y
Remove the zero:
2X = 15Y

Divide each side by '2'.
X = 7.5Y

Simplifying
X = 7.5Y

Subproblem 2
Set the factor '(3X + -1Y)' equal to zero and attempt to solve:

Simplifying
3X + -1Y = 0

Solving
3X + -1Y = 0

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

Add 'Y' to each side of the equation.
3X + -1Y + Y = 0 + Y

Combine like terms: -1Y + Y = 0
3X + 0 = 0 + Y
3X = 0 + Y
Remove the zero:
3X = Y

Divide each side by '3'.
X = 0.3333333333Y

Simplifying
X = 0.3333333333Y
Solution
X = {7.5Y, 0.3333333333Y}

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