9x^2+y^2-z^2-2y+2z=0

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Solution for 9x^2+y^2-z^2-2y+2z=0 equation: 


Simplifying
9x2 + y2 + -1z2 + -2y + 2z = 0

Reorder the terms:
9x2 + -2y + y2 + 2z + -1z2 = 0

Solving
9x2 + -2y + y2 + 2z + -1z2 = 0

Solving for variable 'x'.

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

Add '2y' to each side of the equation.
9x2 + -2y + y2 + 2z + 2y + -1z2 = 0 + 2y

Reorder the terms:
9x2 + -2y + 2y + y2 + 2z + -1z2 = 0 + 2y

Combine like terms: -2y + 2y = 0
9x2 + 0 + y2 + 2z + -1z2 = 0 + 2y
9x2 + y2 + 2z + -1z2 = 0 + 2y
Remove the zero:
9x2 + y2 + 2z + -1z2 = 2y

Add '-1y2' to each side of the equation.
9x2 + y2 + 2z + -1y2 + -1z2 = 2y + -1y2

Reorder the terms:
9x2 + y2 + -1y2 + 2z + -1z2 = 2y + -1y2

Combine like terms: y2 + -1y2 = 0
9x2 + 0 + 2z + -1z2 = 2y + -1y2
9x2 + 2z + -1z2 = 2y + -1y2

Add '-2z' to each side of the equation.
9x2 + 2z + -2z + -1z2 = 2y + -1y2 + -2z

Combine like terms: 2z + -2z = 0
9x2 + 0 + -1z2 = 2y + -1y2 + -2z
9x2 + -1z2 = 2y + -1y2 + -2z

Add 'z2' to each side of the equation.
9x2 + -1z2 + z2 = 2y + -1y2 + -2z + z2

Combine like terms: -1z2 + z2 = 0
9x2 + 0 = 2y + -1y2 + -2z + z2
9x2 = 2y + -1y2 + -2z + z2

Divide each side by '9'.
x2 = 0.2222222222y + -0.1111111111y2 + -0.2222222222z + 0.1111111111z2

Simplifying
x2 = 0.2222222222y + -0.1111111111y2 + -0.2222222222z + 0.1111111111z2

Reorder the terms:
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = 0.2222222222y + -0.2222222222y + -0.1111111111y2 + 0.1111111111y2 + -0.2222222222z + 0.2222222222z + 0.1111111111z2 + -0.1111111111z2

Combine like terms: 0.2222222222y + -0.2222222222y = 0.0000000000
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = 0.0000000000 + -0.1111111111y2 + 0.1111111111y2 + -0.2222222222z + 0.2222222222z + 0.1111111111z2 + -0.1111111111z2
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = -0.1111111111y2 + 0.1111111111y2 + -0.2222222222z + 0.2222222222z + 0.1111111111z2 + -0.1111111111z2

Combine like terms: -0.1111111111y2 + 0.1111111111y2 = 0.0000000000
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = 0.0000000000 + -0.2222222222z + 0.2222222222z + 0.1111111111z2 + -0.1111111111z2
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = -0.2222222222z + 0.2222222222z + 0.1111111111z2 + -0.1111111111z2

Combine like terms: -0.2222222222z + 0.2222222222z = 0.0000000000
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = 0.0000000000 + 0.1111111111z2 + -0.1111111111z2
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = 0.1111111111z2 + -0.1111111111z2

Combine like terms: 0.1111111111z2 + -0.1111111111z2 = 0.0000000000
x2 + -0.2222222222y + 0.1111111111y2 + 0.2222222222z + -0.1111111111z2 = 0.0000000000

The solution to this equation could not be determined.

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