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

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


Simplifying
6y2 + 12y + 6x2 + -12 = -1z2

Reorder the terms:
-12 + 6x2 + 12y + 6y2 = -1z2

Solving
-12 + 6x2 + 12y + 6y2 = -1z2

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 6x2 + 12y + 12 + 6y2 = 12 + -1z2

Reorder the terms:
-12 + 12 + 6x2 + 12y + 6y2 = 12 + -1z2

Combine like terms: -12 + 12 = 0
0 + 6x2 + 12y + 6y2 = 12 + -1z2
6x2 + 12y + 6y2 = 12 + -1z2

Add '-12y' to each side of the equation.
6x2 + 12y + -12y + 6y2 = 12 + -12y + -1z2

Combine like terms: 12y + -12y = 0
6x2 + 0 + 6y2 = 12 + -12y + -1z2
6x2 + 6y2 = 12 + -12y + -1z2

Add '-6y2' to each side of the equation.
6x2 + 6y2 + -6y2 = 12 + -12y + -6y2 + -1z2

Combine like terms: 6y2 + -6y2 = 0
6x2 + 0 = 12 + -12y + -6y2 + -1z2
6x2 = 12 + -12y + -6y2 + -1z2

Divide each side by '6'.
x2 = 2 + -2y + -1y2 + -0.1666666667z2

Simplifying
x2 = 2 + -2y + -1y2 + -0.1666666667z2

Reorder the terms:
-2 + x2 + 2y + y2 + 0.1666666667z2 = 2 + -2y + -1y2 + -0.1666666667z2 + -2 + 2y + y2 + 0.1666666667z2

Reorder the terms:
-2 + x2 + 2y + y2 + 0.1666666667z2 = 2 + -2 + -2y + 2y + -1y2 + y2 + -0.1666666667z2 + 0.1666666667z2

Combine like terms: 2 + -2 = 0
-2 + x2 + 2y + y2 + 0.1666666667z2 = 0 + -2y + 2y + -1y2 + y2 + -0.1666666667z2 + 0.1666666667z2
-2 + x2 + 2y + y2 + 0.1666666667z2 = -2y + 2y + -1y2 + y2 + -0.1666666667z2 + 0.1666666667z2

Combine like terms: -2y + 2y = 0
-2 + x2 + 2y + y2 + 0.1666666667z2 = 0 + -1y2 + y2 + -0.1666666667z2 + 0.1666666667z2
-2 + x2 + 2y + y2 + 0.1666666667z2 = -1y2 + y2 + -0.1666666667z2 + 0.1666666667z2

Combine like terms: -1y2 + y2 = 0
-2 + x2 + 2y + y2 + 0.1666666667z2 = 0 + -0.1666666667z2 + 0.1666666667z2
-2 + x2 + 2y + y2 + 0.1666666667z2 = -0.1666666667z2 + 0.1666666667z2

Combine like terms: -0.1666666667z2 + 0.1666666667z2 = 0.0000000000
-2 + x2 + 2y + y2 + 0.1666666667z2 = 0.0000000000

The solution to this equation could not be determined.

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