y^2-4x^2-z^2+4y+2z=33

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Solution for y^2-4x^2-z^2+4y+2z=33 equation: 


Simplifying
y2 + -4x2 + -1z2 + 4y + 2z = 33

Reorder the terms:
-4x2 + 4y + y2 + 2z + -1z2 = 33

Solving
-4x2 + 4y + y2 + 2z + -1z2 = 33

Solving for variable 'x'.

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

Add '-4y' to each side of the equation.
-4x2 + 4y + y2 + 2z + -4y + -1z2 = 33 + -4y

Reorder the terms:
-4x2 + 4y + -4y + y2 + 2z + -1z2 = 33 + -4y

Combine like terms: 4y + -4y = 0
-4x2 + 0 + y2 + 2z + -1z2 = 33 + -4y
-4x2 + y2 + 2z + -1z2 = 33 + -4y

Add '-1y2' to each side of the equation.
-4x2 + y2 + 2z + -1y2 + -1z2 = 33 + -4y + -1y2

Reorder the terms:
-4x2 + y2 + -1y2 + 2z + -1z2 = 33 + -4y + -1y2

Combine like terms: y2 + -1y2 = 0
-4x2 + 0 + 2z + -1z2 = 33 + -4y + -1y2
-4x2 + 2z + -1z2 = 33 + -4y + -1y2

Add '-2z' to each side of the equation.
-4x2 + 2z + -2z + -1z2 = 33 + -4y + -1y2 + -2z

Combine like terms: 2z + -2z = 0
-4x2 + 0 + -1z2 = 33 + -4y + -1y2 + -2z
-4x2 + -1z2 = 33 + -4y + -1y2 + -2z

Add 'z2' to each side of the equation.
-4x2 + -1z2 + z2 = 33 + -4y + -1y2 + -2z + z2

Combine like terms: -1z2 + z2 = 0
-4x2 + 0 = 33 + -4y + -1y2 + -2z + z2
-4x2 = 33 + -4y + -1y2 + -2z + z2

Divide each side by '-4'.
x2 = -8.25 + y + 0.25y2 + 0.5z + -0.25z2

Simplifying
x2 = -8.25 + y + 0.25y2 + 0.5z + -0.25z2

Reorder the terms:
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = -8.25 + y + 0.25y2 + 0.5z + -0.25z2 + 8.25 + -1y + -0.25y2 + -0.5z + 0.25z2

Reorder the terms:
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = -8.25 + 8.25 + y + -1y + 0.25y2 + -0.25y2 + 0.5z + -0.5z + -0.25z2 + 0.25z2

Combine like terms: -8.25 + 8.25 = 0.00
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = 0.00 + y + -1y + 0.25y2 + -0.25y2 + 0.5z + -0.5z + -0.25z2 + 0.25z2
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = y + -1y + 0.25y2 + -0.25y2 + 0.5z + -0.5z + -0.25z2 + 0.25z2

Combine like terms: y + -1y = 0
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = 0 + 0.25y2 + -0.25y2 + 0.5z + -0.5z + -0.25z2 + 0.25z2
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = 0.25y2 + -0.25y2 + 0.5z + -0.5z + -0.25z2 + 0.25z2

Combine like terms: 0.25y2 + -0.25y2 = 0.00
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = 0.00 + 0.5z + -0.5z + -0.25z2 + 0.25z2
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = 0.5z + -0.5z + -0.25z2 + 0.25z2

Combine like terms: 0.5z + -0.5z = 0.0
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = 0.0 + -0.25z2 + 0.25z2
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = -0.25z2 + 0.25z2

Combine like terms: -0.25z2 + 0.25z2 = 0.00
8.25 + x2 + -1y + -0.25y2 + -0.5z + 0.25z2 = 0.00

The solution to this equation could not be determined.

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