(x^2+4y^2+z^2-4)-(7x^2+y^2)z^3=0

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Solution for (x^2+4y^2+z^2-4)-(7x^2+y^2)z^3=0 equation:


Simplifying
(x2 + 4y2 + z2 + -4) + -1(7x2 + y2) * z3 = 0

Reorder the terms:
(-4 + x2 + 4y2 + z2) + -1(7x2 + y2) * z3 = 0

Remove parenthesis around (-4 + x2 + 4y2 + z2)
-4 + x2 + 4y2 + z2 + -1(7x2 + y2) * z3 = 0

Reorder the terms for easier multiplication:
-4 + x2 + 4y2 + z2 + -1z3(7x2 + y2) = 0
-4 + x2 + 4y2 + z2 + (7x2 * -1z3 + y2 * -1z3) = 0
-4 + x2 + 4y2 + z2 + (-7x2z3 + -1y2z3) = 0

Reorder the terms:
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0

Solving
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + 4 + z2 = 0 + 4

Reorder the terms:
-4 + 4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0 + 4
x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0 + 4

Combine like terms: 0 + 4 = 4
x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 4

Add '-4y2' to each side of the equation.
x2 + -7x2z3 + 4y2 + -1y2z3 + -4y2 + z2 = 4 + -4y2

Reorder the terms:
x2 + -7x2z3 + 4y2 + -4y2 + -1y2z3 + z2 = 4 + -4y2

Combine like terms: 4y2 + -4y2 = 0
x2 + -7x2z3 + 0 + -1y2z3 + z2 = 4 + -4y2
x2 + -7x2z3 + -1y2z3 + z2 = 4 + -4y2

Add 'y2z3' to each side of the equation.
x2 + -7x2z3 + -1y2z3 + y2z3 + z2 = 4 + -4y2 + y2z3

Combine like terms: -1y2z3 + y2z3 = 0
x2 + -7x2z3 + 0 + z2 = 4 + -4y2 + y2z3
x2 + -7x2z3 + z2 = 4 + -4y2 + y2z3

Add '-1z2' to each side of the equation.
x2 + -7x2z3 + z2 + -1z2 = 4 + -4y2 + y2z3 + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + -7x2z3 + 0 = 4 + -4y2 + y2z3 + -1z2
x2 + -7x2z3 = 4 + -4y2 + y2z3 + -1z2

Reorder the terms:
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 4 + -4y2 + y2z3 + -1z2 + -4 + 4y2 + -1y2z3 + z2

Reorder the terms:
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 4 + -4 + -4y2 + 4y2 + y2z3 + -1y2z3 + -1z2 + z2

Combine like terms: 4 + -4 = 0
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0 + -4y2 + 4y2 + y2z3 + -1y2z3 + -1z2 + z2
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = -4y2 + 4y2 + y2z3 + -1y2z3 + -1z2 + z2

Combine like terms: -4y2 + 4y2 = 0
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0 + y2z3 + -1y2z3 + -1z2 + z2
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = y2z3 + -1y2z3 + -1z2 + z2

Combine like terms: y2z3 + -1y2z3 = 0
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0 + -1z2 + z2
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-4 + x2 + -7x2z3 + 4y2 + -1y2z3 + z2 = 0

The solution to this equation could not be determined.

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