x^2+4y^2+z^2=6

Solution for x^2+4y^2+z^2=6 equation:

Simplifying
x2 + 4y2 + z2 = 6

Solving
x2 + 4y2 + z2 = 6

Solving for variable 'x'.

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

Add '-4y2' to each side of the equation.
x2 + 4y2 + -4y2 + z2 = 6 + -4y2

Combine like terms: 4y2 + -4y2 = 0
x2 + 0 + z2 = 6 + -4y2
x2 + z2 = 6 + -4y2

Add '-1z2' to each side of the equation.
x2 + z2 + -1z2 = 6 + -4y2 + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + 0 = 6 + -4y2 + -1z2
x2 = 6 + -4y2 + -1z2

Simplifying
x2 = 6 + -4y2 + -1z2

Reorder the terms:
-6 + x2 + 4y2 + z2 = 6 + -4y2 + -1z2 + -6 + 4y2 + z2

Reorder the terms:
-6 + x2 + 4y2 + z2 = 6 + -6 + -4y2 + 4y2 + -1z2 + z2

Combine like terms: 6 + -6 = 0
-6 + x2 + 4y2 + z2 = 0 + -4y2 + 4y2 + -1z2 + z2
-6 + x2 + 4y2 + z2 = -4y2 + 4y2 + -1z2 + z2

Combine like terms: -4y2 + 4y2 = 0
-6 + x2 + 4y2 + z2 = 0 + -1z2 + z2
-6 + x2 + 4y2 + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-6 + x2 + 4y2 + z2 = 0

The solution to this equation could not be determined.