4x^2-y^2+4z^2-4y-24z+36=0

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Solution for 4x^2-y^2+4z^2-4y-24z+36=0 equation: 


Simplifying
4x2 + -1y2 + 4z2 + -4y + -24z + 36 = 0

Reorder the terms:
36 + 4x2 + -4y + -1y2 + -24z + 4z2 = 0

Solving
36 + 4x2 + -4y + -1y2 + -24z + 4z2 = 0

Solving for variable 'x'.

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

Add '-36' to each side of the equation.
36 + 4x2 + -4y + -1y2 + -24z + -36 + 4z2 = 0 + -36

Reorder the terms:
36 + -36 + 4x2 + -4y + -1y2 + -24z + 4z2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 4x2 + -4y + -1y2 + -24z + 4z2 = 0 + -36
4x2 + -4y + -1y2 + -24z + 4z2 = 0 + -36

Combine like terms: 0 + -36 = -36
4x2 + -4y + -1y2 + -24z + 4z2 = -36

Add '4y' to each side of the equation.
4x2 + -4y + -1y2 + -24z + 4y + 4z2 = -36 + 4y

Reorder the terms:
4x2 + -4y + 4y + -1y2 + -24z + 4z2 = -36 + 4y

Combine like terms: -4y + 4y = 0
4x2 + 0 + -1y2 + -24z + 4z2 = -36 + 4y
4x2 + -1y2 + -24z + 4z2 = -36 + 4y

Add 'y2' to each side of the equation.
4x2 + -1y2 + -24z + y2 + 4z2 = -36 + 4y + y2

Reorder the terms:
4x2 + -1y2 + y2 + -24z + 4z2 = -36 + 4y + y2

Combine like terms: -1y2 + y2 = 0
4x2 + 0 + -24z + 4z2 = -36 + 4y + y2
4x2 + -24z + 4z2 = -36 + 4y + y2

Add '24z' to each side of the equation.
4x2 + -24z + 24z + 4z2 = -36 + 4y + y2 + 24z

Combine like terms: -24z + 24z = 0
4x2 + 0 + 4z2 = -36 + 4y + y2 + 24z
4x2 + 4z2 = -36 + 4y + y2 + 24z

Add '-4z2' to each side of the equation.
4x2 + 4z2 + -4z2 = -36 + 4y + y2 + 24z + -4z2

Combine like terms: 4z2 + -4z2 = 0
4x2 + 0 = -36 + 4y + y2 + 24z + -4z2
4x2 = -36 + 4y + y2 + 24z + -4z2

Divide each side by '4'.
x2 = -9 + y + 0.25y2 + 6z + -1z2

Simplifying
x2 = -9 + y + 0.25y2 + 6z + -1z2

Reorder the terms:
9 + x2 + -1y + -0.25y2 + -6z + z2 = -9 + y + 0.25y2 + 6z + -1z2 + 9 + -1y + -0.25y2 + -6z + z2

Reorder the terms:
9 + x2 + -1y + -0.25y2 + -6z + z2 = -9 + 9 + y + -1y + 0.25y2 + -0.25y2 + 6z + -6z + -1z2 + z2

Combine like terms: -9 + 9 = 0
9 + x2 + -1y + -0.25y2 + -6z + z2 = 0 + y + -1y + 0.25y2 + -0.25y2 + 6z + -6z + -1z2 + z2
9 + x2 + -1y + -0.25y2 + -6z + z2 = y + -1y + 0.25y2 + -0.25y2 + 6z + -6z + -1z2 + z2

Combine like terms: y + -1y = 0
9 + x2 + -1y + -0.25y2 + -6z + z2 = 0 + 0.25y2 + -0.25y2 + 6z + -6z + -1z2 + z2
9 + x2 + -1y + -0.25y2 + -6z + z2 = 0.25y2 + -0.25y2 + 6z + -6z + -1z2 + z2

Combine like terms: 0.25y2 + -0.25y2 = 0.00
9 + x2 + -1y + -0.25y2 + -6z + z2 = 0.00 + 6z + -6z + -1z2 + z2
9 + x2 + -1y + -0.25y2 + -6z + z2 = 6z + -6z + -1z2 + z2

Combine like terms: 6z + -6z = 0
9 + x2 + -1y + -0.25y2 + -6z + z2 = 0 + -1z2 + z2
9 + x2 + -1y + -0.25y2 + -6z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
9 + x2 + -1y + -0.25y2 + -6z + z2 = 0

The solution to this equation could not be determined.

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