(K+1)X^2+(k+1)y^2+2kx+2y+4k+3=0

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Solution for (K+1)X^2+(k+1)y^2+2kx+2y+4k+3=0 equation: 


Simplifying
(K + 1) * X2 + (k + 1) * y2 + 2kx + 2y + 4k + 3 = 0

Reorder the terms:
(1 + K) * X2 + (k + 1) * y2 + 2kx + 2y + 4k + 3 = 0

Reorder the terms for easier multiplication:
X2(1 + K) + (k + 1) * y2 + 2kx + 2y + 4k + 3 = 0
(1 * X2 + K * X2) + (k + 1) * y2 + 2kx + 2y + 4k + 3 = 0

Reorder the terms:
(KX2 + 1X2) + (k + 1) * y2 + 2kx + 2y + 4k + 3 = 0
(KX2 + 1X2) + (k + 1) * y2 + 2kx + 2y + 4k + 3 = 0

Reorder the terms:
KX2 + 1X2 + (1 + k) * y2 + 2kx + 2y + 4k + 3 = 0

Reorder the terms for easier multiplication:
KX2 + 1X2 + y2(1 + k) + 2kx + 2y + 4k + 3 = 0
KX2 + 1X2 + (1 * y2 + k * y2) + 2kx + 2y + 4k + 3 = 0

Reorder the terms:
KX2 + 1X2 + (ky2 + 1y2) + 2kx + 2y + 4k + 3 = 0
KX2 + 1X2 + (ky2 + 1y2) + 2kx + 2y + 4k + 3 = 0

Reorder the terms:
3 + KX2 + 1X2 + 4k + 2kx + ky2 + 2y + 1y2 = 0

Solving
3 + KX2 + 1X2 + 4k + 2kx + ky2 + 2y + 1y2 = 0

Solving for variable 'K'.

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

Add '-3' to each side of the equation.
3 + KX2 + 1X2 + 4k + 2kx + ky2 + 2y + -3 + 1y2 = 0 + -3

Reorder the terms:
3 + -3 + KX2 + 1X2 + 4k + 2kx + ky2 + 2y + 1y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + KX2 + 1X2 + 4k + 2kx + ky2 + 2y + 1y2 = 0 + -3
KX2 + 1X2 + 4k + 2kx + ky2 + 2y + 1y2 = 0 + -3

Combine like terms: 0 + -3 = -3
KX2 + 1X2 + 4k + 2kx + ky2 + 2y + 1y2 = -3

Add '-1X2' to each side of the equation.
KX2 + 1X2 + 4k + 2kx + ky2 + 2y + -1X2 + 1y2 = -3 + -1X2

Reorder the terms:
KX2 + 1X2 + -1X2 + 4k + 2kx + ky2 + 2y + 1y2 = -3 + -1X2

Combine like terms: 1X2 + -1X2 = 0
KX2 + 0 + 4k + 2kx + ky2 + 2y + 1y2 = -3 + -1X2
KX2 + 4k + 2kx + ky2 + 2y + 1y2 = -3 + -1X2

Add '-4k' to each side of the equation.
KX2 + 4k + 2kx + ky2 + 2y + -4k + 1y2 = -3 + -1X2 + -4k

Reorder the terms:
KX2 + 4k + -4k + 2kx + ky2 + 2y + 1y2 = -3 + -1X2 + -4k

Combine like terms: 4k + -4k = 0
KX2 + 0 + 2kx + ky2 + 2y + 1y2 = -3 + -1X2 + -4k
KX2 + 2kx + ky2 + 2y + 1y2 = -3 + -1X2 + -4k

Add '-2kx' to each side of the equation.
KX2 + 2kx + ky2 + 2y + -2kx + 1y2 = -3 + -1X2 + -4k + -2kx

Reorder the terms:
KX2 + 2kx + -2kx + ky2 + 2y + 1y2 = -3 + -1X2 + -4k + -2kx

Combine like terms: 2kx + -2kx = 0
KX2 + 0 + ky2 + 2y + 1y2 = -3 + -1X2 + -4k + -2kx
KX2 + ky2 + 2y + 1y2 = -3 + -1X2 + -4k + -2kx

Add '-1ky2' to each side of the equation.
KX2 + ky2 + 2y + -1ky2 + 1y2 = -3 + -1X2 + -4k + -2kx + -1ky2

Reorder the terms:
KX2 + ky2 + -1ky2 + 2y + 1y2 = -3 + -1X2 + -4k + -2kx + -1ky2

Combine like terms: ky2 + -1ky2 = 0
KX2 + 0 + 2y + 1y2 = -3 + -1X2 + -4k + -2kx + -1ky2
KX2 + 2y + 1y2 = -3 + -1X2 + -4k + -2kx + -1ky2

Add '-2y' to each side of the equation.
KX2 + 2y + -2y + 1y2 = -3 + -1X2 + -4k + -2kx + -1ky2 + -2y

Combine like terms: 2y + -2y = 0
KX2 + 0 + 1y2 = -3 + -1X2 + -4k + -2kx + -1ky2 + -2y
KX2 + 1y2 = -3 + -1X2 + -4k + -2kx + -1ky2 + -2y

Add '-1y2' to each side of the equation.
KX2 + 1y2 + -1y2 = -3 + -1X2 + -4k + -2kx + -1ky2 + -2y + -1y2

Combine like terms: 1y2 + -1y2 = 0
KX2 + 0 = -3 + -1X2 + -4k + -2kx + -1ky2 + -2y + -1y2
KX2 = -3 + -1X2 + -4k + -2kx + -1ky2 + -2y + -1y2

Divide each side by 'X2'.
K = -3X-2 + -1 + -4kX-2 + -2kxX-2 + -1ky2X-2 + -2yX-2 + -1y2X-2

Simplifying
K = -3X-2 + -1 + -4kX-2 + -2kxX-2 + -1ky2X-2 + -2yX-2 + -1y2X-2

Reorder the terms:
K = -1 + -3X-2 + -4kX-2 + -2kxX-2 + -1ky2X-2 + -2yX-2 + -1y2X-2

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