3x^2+3y^2+3z^2=10+6y+12z

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Solution for 3x^2+3y^2+3z^2=10+6y+12z equation: 


Simplifying
3x2 + 3y2 + 3z2 = 10 + 6y + 12z

Solving
3x2 + 3y2 + 3z2 = 10 + 6y + 12z

Solving for variable 'x'.

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

Add '-3y2' to each side of the equation.
3x2 + 3y2 + -3y2 + 3z2 = 10 + 6y + -3y2 + 12z

Combine like terms: 3y2 + -3y2 = 0
3x2 + 0 + 3z2 = 10 + 6y + -3y2 + 12z
3x2 + 3z2 = 10 + 6y + -3y2 + 12z

Add '-3z2' to each side of the equation.
3x2 + 3z2 + -3z2 = 10 + 6y + -3y2 + 12z + -3z2

Combine like terms: 3z2 + -3z2 = 0
3x2 + 0 = 10 + 6y + -3y2 + 12z + -3z2
3x2 = 10 + 6y + -3y2 + 12z + -3z2

Divide each side by '3'.
x2 = 3.333333333 + 2y + -1y2 + 4z + -1z2

Simplifying
x2 = 3.333333333 + 2y + -1y2 + 4z + -1z2

Reorder the terms:
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 3.333333333 + 2y + -1y2 + 4z + -1z2 + -3.333333333 + -2y + y2 + -4z + z2

Reorder the terms:
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 3.333333333 + -3.333333333 + 2y + -2y + -1y2 + y2 + 4z + -4z + -1z2 + z2

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 0.000000000 + 2y + -2y + -1y2 + y2 + 4z + -4z + -1z2 + z2
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 2y + -2y + -1y2 + y2 + 4z + -4z + -1z2 + z2

Combine like terms: 2y + -2y = 0
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 0 + -1y2 + y2 + 4z + -4z + -1z2 + z2
-3.333333333 + x2 + -2y + y2 + -4z + z2 = -1y2 + y2 + 4z + -4z + -1z2 + z2

Combine like terms: -1y2 + y2 = 0
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 0 + 4z + -4z + -1z2 + z2
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 4z + -4z + -1z2 + z2

Combine like terms: 4z + -4z = 0
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 0 + -1z2 + z2
-3.333333333 + x2 + -2y + y2 + -4z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-3.333333333 + x2 + -2y + y2 + -4z + z2 = 0

The solution to this equation could not be determined.

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