(Y+2)(y+2)=(x-6)(x-6)+(y-6)(y-6)

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Solution for (Y+2)(y+2)=(x-6)(x-6)+(y-6)(y-6) equation: 


Simplifying
(Y + 2)(y + 2) = (x + -6)(x + -6) + (y + -6)(y + -6)

Reorder the terms:
(2 + Y)(y + 2) = (x + -6)(x + -6) + (y + -6)(y + -6)

Reorder the terms:
(2 + Y)(2 + y) = (x + -6)(x + -6) + (y + -6)(y + -6)

Multiply (2 + Y) * (2 + y)
(2(2 + y) + Y(2 + y)) = (x + -6)(x + -6) + (y + -6)(y + -6)
((2 * 2 + y * 2) + Y(2 + y)) = (x + -6)(x + -6) + (y + -6)(y + -6)
((4 + 2y) + Y(2 + y)) = (x + -6)(x + -6) + (y + -6)(y + -6)
(4 + 2y + (2 * Y + y * Y)) = (x + -6)(x + -6) + (y + -6)(y + -6)
(4 + 2y + (2Y + yY)) = (x + -6)(x + -6) + (y + -6)(y + -6)

Reorder the terms:
(4 + 2Y + 2y + yY) = (x + -6)(x + -6) + (y + -6)(y + -6)
(4 + 2Y + 2y + yY) = (x + -6)(x + -6) + (y + -6)(y + -6)

Reorder the terms:
4 + 2Y + 2y + yY = (-6 + x)(x + -6) + (y + -6)(y + -6)

Reorder the terms:
4 + 2Y + 2y + yY = (-6 + x)(-6 + x) + (y + -6)(y + -6)

Multiply (-6 + x) * (-6 + x)
4 + 2Y + 2y + yY = (-6(-6 + x) + x(-6 + x)) + (y + -6)(y + -6)
4 + 2Y + 2y + yY = ((-6 * -6 + x * -6) + x(-6 + x)) + (y + -6)(y + -6)
4 + 2Y + 2y + yY = ((36 + -6x) + x(-6 + x)) + (y + -6)(y + -6)
4 + 2Y + 2y + yY = (36 + -6x + (-6 * x + x * x)) + (y + -6)(y + -6)
4 + 2Y + 2y + yY = (36 + -6x + (-6x + x2)) + (y + -6)(y + -6)

Combine like terms: -6x + -6x = -12x
4 + 2Y + 2y + yY = (36 + -12x + x2) + (y + -6)(y + -6)

Reorder the terms:
4 + 2Y + 2y + yY = 36 + -12x + x2 + (-6 + y)(y + -6)

Reorder the terms:
4 + 2Y + 2y + yY = 36 + -12x + x2 + (-6 + y)(-6 + y)

Multiply (-6 + y) * (-6 + y)
4 + 2Y + 2y + yY = 36 + -12x + x2 + (-6(-6 + y) + y(-6 + y))
4 + 2Y + 2y + yY = 36 + -12x + x2 + ((-6 * -6 + y * -6) + y(-6 + y))
4 + 2Y + 2y + yY = 36 + -12x + x2 + ((36 + -6y) + y(-6 + y))
4 + 2Y + 2y + yY = 36 + -12x + x2 + (36 + -6y + (-6 * y + y * y))
4 + 2Y + 2y + yY = 36 + -12x + x2 + (36 + -6y + (-6y + y2))

Combine like terms: -6y + -6y = -12y
4 + 2Y + 2y + yY = 36 + -12x + x2 + (36 + -12y + y2)

Reorder the terms:
4 + 2Y + 2y + yY = 36 + 36 + -12x + x2 + -12y + y2

Combine like terms: 36 + 36 = 72
4 + 2Y + 2y + yY = 72 + -12x + x2 + -12y + y2

Solving
4 + 2Y + 2y + yY = 72 + -12x + x2 + -12y + y2

Solving for variable 'Y'.

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

Add '-4' to each side of the equation.
4 + 2Y + 2y + -4 + yY = 72 + -12x + x2 + -12y + -4 + y2

Reorder the terms:
4 + -4 + 2Y + 2y + yY = 72 + -12x + x2 + -12y + -4 + y2

Combine like terms: 4 + -4 = 0
0 + 2Y + 2y + yY = 72 + -12x + x2 + -12y + -4 + y2
2Y + 2y + yY = 72 + -12x + x2 + -12y + -4 + y2

Reorder the terms:
2Y + 2y + yY = 72 + -4 + -12x + x2 + -12y + y2

Combine like terms: 72 + -4 = 68
2Y + 2y + yY = 68 + -12x + x2 + -12y + y2

Add '-2y' to each side of the equation.
2Y + 2y + -2y + yY = 68 + -12x + x2 + -12y + -2y + y2

Combine like terms: 2y + -2y = 0
2Y + 0 + yY = 68 + -12x + x2 + -12y + -2y + y2
2Y + yY = 68 + -12x + x2 + -12y + -2y + y2

Combine like terms: -12y + -2y = -14y
2Y + yY = 68 + -12x + x2 + -14y + y2

Reorder the terms:
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = 68 + -12x + x2 + -14y + y2 + -68 + 12x + -1x2 + 14y + -1y2

Reorder the terms:
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = 68 + -68 + -12x + 12x + x2 + -1x2 + -14y + 14y + y2 + -1y2

Combine like terms: 68 + -68 = 0
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = 0 + -12x + 12x + x2 + -1x2 + -14y + 14y + y2 + -1y2
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = -12x + 12x + x2 + -1x2 + -14y + 14y + y2 + -1y2

Combine like terms: -12x + 12x = 0
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = 0 + x2 + -1x2 + -14y + 14y + y2 + -1y2
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = x2 + -1x2 + -14y + 14y + y2 + -1y2

Combine like terms: x2 + -1x2 = 0
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = 0 + -14y + 14y + y2 + -1y2
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = -14y + 14y + y2 + -1y2

Combine like terms: -14y + 14y = 0
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = 0 + y2 + -1y2
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-68 + 2Y + 12x + -1x2 + 14y + yY + -1y2 = 0

The solution to this equation could not be determined.

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