-1.00701051577(x^2-y^2-z^2+xy)=x^2+3y^2+3z^2-3xy-2xz-2yz

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Solution for -1.00701051577(x^2-y^2-z^2+xy)=x^2+3y^2+3z^2-3xy-2xz-2yz equation: 


Simplifying
-1.00701051577(x2 + -1y2 + -1z2 + xy) = x2 + 3y2 + 3z2 + -3xy + -2xz + -2yz

Reorder the terms:
-1.00701051577(xy + x2 + -1y2 + -1z2) = x2 + 3y2 + 3z2 + -3xy + -2xz + -2yz
(xy * -1.00701051577 + x2 * -1.00701051577 + -1y2 * -1.00701051577 + -1z2 * -1.00701051577) = x2 + 3y2 + 3z2 + -3xy + -2xz + -2yz
(-1.00701051577xy + -1.00701051577x2 + 1.007010516y2 + 1.007010516z2) = x2 + 3y2 + 3z2 + -3xy + -2xz + -2yz

Reorder the terms:
-1.00701051577xy + -1.00701051577x2 + 1.007010516y2 + 1.007010516z2 = -3xy + -2xz + x2 + -2yz + 3y2 + 3z2

Solving
-1.00701051577xy + -1.00701051577x2 + 1.007010516y2 + 1.007010516z2 = -3xy + -2xz + x2 + -2yz + 3y2 + 3z2

Solving for variable 'x'.

Reorder the terms:
-1.00701051577xy + 3xy + 2xz + -1.00701051577x2 + -1x2 + 2yz + 1.007010516y2 + -3y2 + 1.007010516z2 + -3z2 = -3xy + -2xz + x2 + -2yz + 3y2 + 3z2 + 3xy + 2xz + -1x2 + 2yz + -3y2 + -3z2

Combine like terms: -1.00701051577xy + 3xy = 1.99298948423xy
1.99298948423xy + 2xz + -1.00701051577x2 + -1x2 + 2yz + 1.007010516y2 + -3y2 + 1.007010516z2 + -3z2 = -3xy + -2xz + x2 + -2yz + 3y2 + 3z2 + 3xy + 2xz + -1x2 + 2yz + -3y2 + -3z2

Combine like terms: -1.00701051577x2 + -1x2 = -2.00701051577x2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + 1.007010516y2 + -3y2 + 1.007010516z2 + -3z2 = -3xy + -2xz + x2 + -2yz + 3y2 + 3z2 + 3xy + 2xz + -1x2 + 2yz + -3y2 + -3z2

Combine like terms: 1.007010516y2 + -3y2 = -1.992989484y2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + 1.007010516z2 + -3z2 = -3xy + -2xz + x2 + -2yz + 3y2 + 3z2 + 3xy + 2xz + -1x2 + 2yz + -3y2 + -3z2

Combine like terms: 1.007010516z2 + -3z2 = -1.992989484z2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = -3xy + -2xz + x2 + -2yz + 3y2 + 3z2 + 3xy + 2xz + -1x2 + 2yz + -3y2 + -3z2

Reorder the terms:
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = -3xy + 3xy + -2xz + 2xz + x2 + -1x2 + -2yz + 2yz + 3y2 + -3y2 + 3z2 + -3z2

Combine like terms: -3xy + 3xy = 0
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 0 + -2xz + 2xz + x2 + -1x2 + -2yz + 2yz + 3y2 + -3y2 + 3z2 + -3z2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = -2xz + 2xz + x2 + -1x2 + -2yz + 2yz + 3y2 + -3y2 + 3z2 + -3z2

Combine like terms: -2xz + 2xz = 0
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 0 + x2 + -1x2 + -2yz + 2yz + 3y2 + -3y2 + 3z2 + -3z2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = x2 + -1x2 + -2yz + 2yz + 3y2 + -3y2 + 3z2 + -3z2

Combine like terms: x2 + -1x2 = 0
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 0 + -2yz + 2yz + 3y2 + -3y2 + 3z2 + -3z2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = -2yz + 2yz + 3y2 + -3y2 + 3z2 + -3z2

Combine like terms: -2yz + 2yz = 0
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 0 + 3y2 + -3y2 + 3z2 + -3z2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 3y2 + -3y2 + 3z2 + -3z2

Combine like terms: 3y2 + -3y2 = 0
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 0 + 3z2 + -3z2
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 3z2 + -3z2

Combine like terms: 3z2 + -3z2 = 0
1.99298948423xy + 2xz + -2.00701051577x2 + 2yz + -1.992989484y2 + -1.992989484z2 = 0

The solution to this equation could not be determined.

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