x^2+y^2+z^2-6y+8z=0

Solution for x^2+y^2+z^2-6y+8z=0 equation:

Simplifying
x2 + y2 + z2 + -6y + 8z = 0

Reorder the terms:
x2 + -6y + y2 + 8z + z2 = 0

Solving
x2 + -6y + y2 + 8z + z2 = 0

Solving for variable 'x'.

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

Add '6y' to each side of the equation.
x2 + -6y + y2 + 8z + 6y + z2 = 0 + 6y

Reorder the terms:
x2 + -6y + 6y + y2 + 8z + z2 = 0 + 6y

Combine like terms: -6y + 6y = 0
x2 + 0 + y2 + 8z + z2 = 0 + 6y
x2 + y2 + 8z + z2 = 0 + 6y
Remove the zero:
x2 + y2 + 8z + z2 = 6y

Add '-1y2' to each side of the equation.
x2 + y2 + 8z + -1y2 + z2 = 6y + -1y2

Reorder the terms:
x2 + y2 + -1y2 + 8z + z2 = 6y + -1y2

Combine like terms: y2 + -1y2 = 0
x2 + 0 + 8z + z2 = 6y + -1y2
x2 + 8z + z2 = 6y + -1y2

Add '-8z' to each side of the equation.
x2 + 8z + -8z + z2 = 6y + -1y2 + -8z

Combine like terms: 8z + -8z = 0
x2 + 0 + z2 = 6y + -1y2 + -8z
x2 + z2 = 6y + -1y2 + -8z

Add '-1z2' to each side of the equation.
x2 + z2 + -1z2 = 6y + -1y2 + -8z + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + 0 = 6y + -1y2 + -8z + -1z2
x2 = 6y + -1y2 + -8z + -1z2

Simplifying
x2 = 6y + -1y2 + -8z + -1z2

Reorder the terms:
x2 + -6y + y2 + 8z + z2 = 6y + -6y + -1y2 + y2 + -8z + 8z + -1z2 + z2

Combine like terms: 6y + -6y = 0
x2 + -6y + y2 + 8z + z2 = 0 + -1y2 + y2 + -8z + 8z + -1z2 + z2
x2 + -6y + y2 + 8z + z2 = -1y2 + y2 + -8z + 8z + -1z2 + z2

Combine like terms: -1y2 + y2 = 0
x2 + -6y + y2 + 8z + z2 = 0 + -8z + 8z + -1z2 + z2
x2 + -6y + y2 + 8z + z2 = -8z + 8z + -1z2 + z2

Combine like terms: -8z + 8z = 0
x2 + -6y + y2 + 8z + z2 = 0 + -1z2 + z2
x2 + -6y + y2 + 8z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
x2 + -6y + y2 + 8z + z2 = 0

The solution to this equation could not be determined.