9x^2-y^2+6yz-9z^2=0

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Solution for 9x^2-y^2+6yz-9z^2=0 equation: 


Simplifying
9x2 + -1y2 + 6yz + -9z2 = 0

Reorder the terms:
9x2 + 6yz + -1y2 + -9z2 = 0

Solving
9x2 + 6yz + -1y2 + -9z2 = 0

Solving for variable 'x'.

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

Add '-6yz' to each side of the equation.
9x2 + 6yz + -1y2 + -6yz + -9z2 = 0 + -6yz

Reorder the terms:
9x2 + 6yz + -6yz + -1y2 + -9z2 = 0 + -6yz

Combine like terms: 6yz + -6yz = 0
9x2 + 0 + -1y2 + -9z2 = 0 + -6yz
9x2 + -1y2 + -9z2 = 0 + -6yz
Remove the zero:
9x2 + -1y2 + -9z2 = -6yz

Add 'y2' to each side of the equation.
9x2 + -1y2 + y2 + -9z2 = -6yz + y2

Combine like terms: -1y2 + y2 = 0
9x2 + 0 + -9z2 = -6yz + y2
9x2 + -9z2 = -6yz + y2

Add '9z2' to each side of the equation.
9x2 + -9z2 + 9z2 = -6yz + y2 + 9z2

Combine like terms: -9z2 + 9z2 = 0
9x2 + 0 = -6yz + y2 + 9z2
9x2 = -6yz + y2 + 9z2

Divide each side by '9'.
x2 = -0.6666666667yz + 0.1111111111y2 + z2

Simplifying
x2 = -0.6666666667yz + 0.1111111111y2 + z2

Reorder the terms:
x2 + 0.6666666667yz + -0.1111111111y2 + -1z2 = -0.6666666667yz + 0.6666666667yz + 0.1111111111y2 + -0.1111111111y2 + z2 + -1z2

Combine like terms: -0.6666666667yz + 0.6666666667yz = 0.0000000000
x2 + 0.6666666667yz + -0.1111111111y2 + -1z2 = 0.0000000000 + 0.1111111111y2 + -0.1111111111y2 + z2 + -1z2
x2 + 0.6666666667yz + -0.1111111111y2 + -1z2 = 0.1111111111y2 + -0.1111111111y2 + z2 + -1z2

Combine like terms: 0.1111111111y2 + -0.1111111111y2 = 0.0000000000
x2 + 0.6666666667yz + -0.1111111111y2 + -1z2 = 0.0000000000 + z2 + -1z2
x2 + 0.6666666667yz + -0.1111111111y2 + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + 0.6666666667yz + -0.1111111111y2 + -1z2 = 0

The solution to this equation could not be determined.

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