3*x^2+5*y^2+5*z^2-2*x*y*sqrt(6)-2*y*z*sqrt(15)=0

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Solution for 3*x^2+5*y^2+5*z^2-2*x*y*sqrt(6)-2*y*z*sqrt(15)=0 equation: 


Simplifying
3x2 + 5y2 + 5z2 + -2x * y * sqrt(6) + -2y * z * sqrt(15) = 0

Reorder the terms for easier multiplication:
3x2 + 5y2 + 5z2 + -2 * 6x * y * qrst + -2y * z * sqrt(15) = 0

Multiply -2 * 6
3x2 + 5y2 + 5z2 + -12x * y * qrst + -2y * z * sqrt(15) = 0

Multiply x * y
3x2 + 5y2 + 5z2 + -12xy * qrst + -2y * z * sqrt(15) = 0

Multiply xy * qrst
3x2 + 5y2 + 5z2 + -12qrstxy + -2y * z * sqrt(15) = 0

Reorder the terms for easier multiplication:
3x2 + 5y2 + 5z2 + -12qrstxy + -2 * 15y * z * qrst = 0

Multiply -2 * 15
3x2 + 5y2 + 5z2 + -12qrstxy + -30y * z * qrst = 0

Multiply y * z
3x2 + 5y2 + 5z2 + -12qrstxy + -30yz * qrst = 0

Multiply yz * qrst
3x2 + 5y2 + 5z2 + -12qrstxy + -30qrstyz = 0

Reorder the terms:
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = 0

Solving
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = 0

Solving for variable 'q'.

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

Add '-3x2' to each side of the equation.
-12qrstxy + -30qrstyz + 3x2 + 5y2 + -3x2 + 5z2 = 0 + -3x2

Reorder the terms:
-12qrstxy + -30qrstyz + 3x2 + -3x2 + 5y2 + 5z2 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12qrstxy + -30qrstyz + 0 + 5y2 + 5z2 = 0 + -3x2
-12qrstxy + -30qrstyz + 5y2 + 5z2 = 0 + -3x2
Remove the zero:
-12qrstxy + -30qrstyz + 5y2 + 5z2 = -3x2

Add '-5y2' to each side of the equation.
-12qrstxy + -30qrstyz + 5y2 + -5y2 + 5z2 = -3x2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-12qrstxy + -30qrstyz + 0 + 5z2 = -3x2 + -5y2
-12qrstxy + -30qrstyz + 5z2 = -3x2 + -5y2

Add '-5z2' to each side of the equation.
-12qrstxy + -30qrstyz + 5z2 + -5z2 = -3x2 + -5y2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
-12qrstxy + -30qrstyz + 0 = -3x2 + -5y2 + -5z2
-12qrstxy + -30qrstyz = -3x2 + -5y2 + -5z2

Reorder the terms:
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = -3x2 + 3x2 + -5y2 + 5y2 + -5z2 + 5z2

Combine like terms: -3x2 + 3x2 = 0
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = 0 + -5y2 + 5y2 + -5z2 + 5z2
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = -5y2 + 5y2 + -5z2 + 5z2

Combine like terms: -5y2 + 5y2 = 0
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = 0 + -5z2 + 5z2
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = -5z2 + 5z2

Combine like terms: -5z2 + 5z2 = 0
-12qrstxy + -30qrstyz + 3x2 + 5y2 + 5z2 = 0

The solution to this equation could not be determined.

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