4x^2+12xy+9y^2-4r^2=0

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Solution for 4x^2+12xy+9y^2-4r^2=0 equation: 


Simplifying
4x2 + 12xy + 9y2 + -4r2 = 0

Reorder the terms:
-4r2 + 12xy + 4x2 + 9y2 = 0

Solving
-4r2 + 12xy + 4x2 + 9y2 = 0

Solving for variable 'r'.

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

Add '-12xy' to each side of the equation.
-4r2 + 12xy + 4x2 + -12xy + 9y2 = 0 + -12xy

Reorder the terms:
-4r2 + 12xy + -12xy + 4x2 + 9y2 = 0 + -12xy

Combine like terms: 12xy + -12xy = 0
-4r2 + 0 + 4x2 + 9y2 = 0 + -12xy
-4r2 + 4x2 + 9y2 = 0 + -12xy
Remove the zero:
-4r2 + 4x2 + 9y2 = -12xy

Add '-4x2' to each side of the equation.
-4r2 + 4x2 + -4x2 + 9y2 = -12xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4r2 + 0 + 9y2 = -12xy + -4x2
-4r2 + 9y2 = -12xy + -4x2

Add '-9y2' to each side of the equation.
-4r2 + 9y2 + -9y2 = -12xy + -4x2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
-4r2 + 0 = -12xy + -4x2 + -9y2
-4r2 = -12xy + -4x2 + -9y2

Divide each side by '-4'.
r2 = 3xy + x2 + 2.25y2

Simplifying
r2 = 3xy + x2 + 2.25y2

Reorder the terms:
r2 + -3xy + -1x2 + -2.25y2 = 3xy + -3xy + x2 + -1x2 + 2.25y2 + -2.25y2

Combine like terms: 3xy + -3xy = 0
r2 + -3xy + -1x2 + -2.25y2 = 0 + x2 + -1x2 + 2.25y2 + -2.25y2
r2 + -3xy + -1x2 + -2.25y2 = x2 + -1x2 + 2.25y2 + -2.25y2

Combine like terms: x2 + -1x2 = 0
r2 + -3xy + -1x2 + -2.25y2 = 0 + 2.25y2 + -2.25y2
r2 + -3xy + -1x2 + -2.25y2 = 2.25y2 + -2.25y2

Combine like terms: 2.25y2 + -2.25y2 = 0.00
r2 + -3xy + -1x2 + -2.25y2 = 0.00

The solution to this equation could not be determined.

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