((x*x)+(y*y))+(z+z)=2(-3x+4y-5z)-50

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Solution for ((x*x)+(y*y))+(z+z)=2(-3x+4y-5z)-50 equation: 


Simplifying
((x * x) + (y * y)) + (z + z) = 2(-3x + 4y + -5z) + -50

Multiply x * x
((x2) + (y * y)) + (z + z) = 2(-3x + 4y + -5z) + -50
(x2 + (y * y)) + (z + z) = 2(-3x + 4y + -5z) + -50

Multiply y * y
(x2 + (y2)) + (z + z) = 2(-3x + 4y + -5z) + -50
(x2 + y2) + (z + z) = 2(-3x + 4y + -5z) + -50

Remove parenthesis around (x2 + y2)
x2 + y2 + (z + z) = 2(-3x + 4y + -5z) + -50

Combine like terms: z + z = 2z
x2 + y2 + (2z) = 2(-3x + 4y + -5z) + -50
x2 + y2 + (2z) = 2(-3x + 4y + -5z) + -50
x2 + y2 + (2z) = (-3x * 2 + 4y * 2 + -5z * 2) + -50
x2 + y2 + (2z) = (-6x + 8y + -10z) + -50

Reorder the terms:
x2 + y2 + (2z) = -50 + -6x + 8y + -10z

Solving
x2 + y2 + (2z) = -50 + -6x + 8y + -10z

Solving for variable 'x'.

Reorder the terms:
50 + 6x + x2 + -8y + y2 + (2z) + 10z = -50 + -6x + 8y + -10z + 50 + 6x + -8y + 10z

Combine like terms: (2z) + 10z = 12z
50 + 6x + x2 + -8y + y2 + 12z = -50 + -6x + 8y + -10z + 50 + 6x + -8y + 10z

Reorder the terms:
50 + 6x + x2 + -8y + y2 + 12z = -50 + 50 + -6x + 6x + 8y + -8y + -10z + 10z

Combine like terms: -50 + 50 = 0
50 + 6x + x2 + -8y + y2 + 12z = 0 + -6x + 6x + 8y + -8y + -10z + 10z
50 + 6x + x2 + -8y + y2 + 12z = -6x + 6x + 8y + -8y + -10z + 10z

Combine like terms: -6x + 6x = 0
50 + 6x + x2 + -8y + y2 + 12z = 0 + 8y + -8y + -10z + 10z
50 + 6x + x2 + -8y + y2 + 12z = 8y + -8y + -10z + 10z

Combine like terms: 8y + -8y = 0
50 + 6x + x2 + -8y + y2 + 12z = 0 + -10z + 10z
50 + 6x + x2 + -8y + y2 + 12z = -10z + 10z

Combine like terms: -10z + 10z = 0
50 + 6x + x2 + -8y + y2 + 12z = 0

The solution to this equation could not be determined.

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