3x^2+2y^2+6z^2=12

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Solution for 3x^2+2y^2+6z^2=12 equation: 


Simplifying
3x2 + 2y2 + 6z2 = 12

Solving
3x2 + 2y2 + 6z2 = 12

Solving for variable 'x'.

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

Add '-2y2' to each side of the equation.
3x2 + 2y2 + -2y2 + 6z2 = 12 + -2y2

Combine like terms: 2y2 + -2y2 = 0
3x2 + 0 + 6z2 = 12 + -2y2
3x2 + 6z2 = 12 + -2y2

Add '-6z2' to each side of the equation.
3x2 + 6z2 + -6z2 = 12 + -2y2 + -6z2

Combine like terms: 6z2 + -6z2 = 0
3x2 + 0 = 12 + -2y2 + -6z2
3x2 = 12 + -2y2 + -6z2

Divide each side by '3'.
x2 = 4 + -0.6666666667y2 + -2z2

Simplifying
x2 = 4 + -0.6666666667y2 + -2z2

Reorder the terms:
-4 + x2 + 0.6666666667y2 + 2z2 = 4 + -0.6666666667y2 + -2z2 + -4 + 0.6666666667y2 + 2z2

Reorder the terms:
-4 + x2 + 0.6666666667y2 + 2z2 = 4 + -4 + -0.6666666667y2 + 0.6666666667y2 + -2z2 + 2z2

Combine like terms: 4 + -4 = 0
-4 + x2 + 0.6666666667y2 + 2z2 = 0 + -0.6666666667y2 + 0.6666666667y2 + -2z2 + 2z2
-4 + x2 + 0.6666666667y2 + 2z2 = -0.6666666667y2 + 0.6666666667y2 + -2z2 + 2z2

Combine like terms: -0.6666666667y2 + 0.6666666667y2 = 0.0000000000
-4 + x2 + 0.6666666667y2 + 2z2 = 0.0000000000 + -2z2 + 2z2
-4 + x2 + 0.6666666667y2 + 2z2 = -2z2 + 2z2

Combine like terms: -2z2 + 2z2 = 0
-4 + x2 + 0.6666666667y2 + 2z2 = 0

The solution to this equation could not be determined.

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