(x^2+2x+4)(y^2-2y+3)=z^2+4z+2

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Solution for (x^2+2x+4)(y^2-2y+3)=z^2+4z+2 equation: 


Simplifying
(x2 + 2x + 4)(y2 + -2y + 3) = z2 + 4z + 2

Reorder the terms:
(4 + 2x + x2)(y2 + -2y + 3) = z2 + 4z + 2

Reorder the terms:
(4 + 2x + x2)(3 + -2y + y2) = z2 + 4z + 2

Multiply (4 + 2x + x2) * (3 + -2y + y2)
(4(3 + -2y + y2) + 2x * (3 + -2y + y2) + x2(3 + -2y + y2)) = z2 + 4z + 2
((3 * 4 + -2y * 4 + y2 * 4) + 2x * (3 + -2y + y2) + x2(3 + -2y + y2)) = z2 + 4z + 2
((12 + -8y + 4y2) + 2x * (3 + -2y + y2) + x2(3 + -2y + y2)) = z2 + 4z + 2
(12 + -8y + 4y2 + (3 * 2x + -2y * 2x + y2 * 2x) + x2(3 + -2y + y2)) = z2 + 4z + 2
(12 + -8y + 4y2 + (6x + -4xy + 2xy2) + x2(3 + -2y + y2)) = z2 + 4z + 2
(12 + -8y + 4y2 + 6x + -4xy + 2xy2 + (3 * x2 + -2y * x2 + y2 * x2)) = z2 + 4z + 2
(12 + -8y + 4y2 + 6x + -4xy + 2xy2 + (3x2 + -2x2y + x2y2)) = z2 + 4z + 2

Reorder the terms:
(12 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2) = z2 + 4z + 2
(12 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2) = z2 + 4z + 2

Reorder the terms:
12 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 = 2 + 4z + z2

Solving
12 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 = 2 + 4z + z2

Solving for variable 'x'.

Reorder the terms:
12 + -2 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = 2 + 4z + z2 + -2 + -4z + -1z2

Combine like terms: 12 + -2 = 10
10 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = 2 + 4z + z2 + -2 + -4z + -1z2

Reorder the terms:
10 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = 2 + -2 + 4z + -4z + z2 + -1z2

Combine like terms: 2 + -2 = 0
10 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = 0 + 4z + -4z + z2 + -1z2
10 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = 4z + -4z + z2 + -1z2

Combine like terms: 4z + -4z = 0
10 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = 0 + z2 + -1z2
10 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
10 + 6x + -4xy + 2xy2 + 3x2 + -2x2y + x2y2 + -8y + 4y2 + -4z + -1z2 = 0

The solution to this equation could not be determined.

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