=3r^4-r^3t-4r^2t^2+6rt^2+4r^2t^2-4rt^3(6x^2+2xy-y^2)+(4x^2-9xy-3y^2)

Simple and best practice solution for =3r^4-r^3t-4r^2t^2+6rt^2+4r^2t^2-4rt^3(6x^2+2xy-y^2)+(4x^2-9xy-3y^2) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solut

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Solution for =3r^4-r^3t-4r^2t^2+6rt^2+4r^2t^2-4rt^3(6x^2+2xy-y^2)+(4x^2-9xy-3y^2) equation:


Simplifying
0 = 3r4 + -1r3t + -4r2t2 + 6rt2 + 4r2t2 + -4rt3(6x2 + 2xy + -1y2) + (4x2 + -9xy + -3y2)

Reorder the terms:
0 = 3r4 + -1r3t + -4r2t2 + 6rt2 + 4r2t2 + -4rt3(2xy + 6x2 + -1y2) + (4x2 + -9xy + -3y2)
0 = 3r4 + -1r3t + -4r2t2 + 6rt2 + 4r2t2 + (2xy * -4rt3 + 6x2 * -4rt3 + -1y2 * -4rt3) + (4x2 + -9xy + -3y2)
0 = 3r4 + -1r3t + -4r2t2 + 6rt2 + 4r2t2 + (-8rt3xy + -24rt3x2 + 4rt3y2) + (4x2 + -9xy + -3y2)

Reorder the terms:
0 = 3r4 + -1r3t + -4r2t2 + 6rt2 + 4r2t2 + -8rt3xy + -24rt3x2 + 4rt3y2 + (-9xy + 4x2 + -3y2)

Remove parenthesis around (-9xy + 4x2 + -3y2)
0 = 3r4 + -1r3t + -4r2t2 + 6rt2 + 4r2t2 + -8rt3xy + -24rt3x2 + 4rt3y2 + -9xy + 4x2 + -3y2

Reorder the terms:
0 = 6rt2 + -8rt3xy + -24rt3x2 + 4rt3y2 + -4r2t2 + 4r2t2 + -1r3t + 3r4 + -9xy + 4x2 + -3y2

Combine like terms: -4r2t2 + 4r2t2 = 0
0 = 6rt2 + -8rt3xy + -24rt3x2 + 4rt3y2 + 0 + -1r3t + 3r4 + -9xy + 4x2 + -3y2
0 = 6rt2 + -8rt3xy + -24rt3x2 + 4rt3y2 + -1r3t + 3r4 + -9xy + 4x2 + -3y2

Solving
0 = 6rt2 + -8rt3xy + -24rt3x2 + 4rt3y2 + -1r3t + 3r4 + -9xy + 4x2 + -3y2

Solving for variable 'r'.
Remove the zero:
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 6rt2 + -8rt3xy + -24rt3x2 + 4rt3y2 + -1r3t + 3r4 + -9xy + 4x2 + -3y2 + -6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2

Reorder the terms:
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 6rt2 + -6rt2 + -8rt3xy + 8rt3xy + -24rt3x2 + 24rt3x2 + 4rt3y2 + -4rt3y2 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: 6rt2 + -6rt2 = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + -8rt3xy + 8rt3xy + -24rt3x2 + 24rt3x2 + 4rt3y2 + -4rt3y2 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = -8rt3xy + 8rt3xy + -24rt3x2 + 24rt3x2 + 4rt3y2 + -4rt3y2 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: -8rt3xy + 8rt3xy = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + -24rt3x2 + 24rt3x2 + 4rt3y2 + -4rt3y2 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = -24rt3x2 + 24rt3x2 + 4rt3y2 + -4rt3y2 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: -24rt3x2 + 24rt3x2 = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + 4rt3y2 + -4rt3y2 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 4rt3y2 + -4rt3y2 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: 4rt3y2 + -4rt3y2 = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = -1r3t + r3t + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: -1r3t + r3t = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 3r4 + -3r4 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: 3r4 + -3r4 = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = -9xy + 9xy + 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: -9xy + 9xy = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + 4x2 + -4x2 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 4x2 + -4x2 + -3y2 + 3y2

Combine like terms: 4x2 + -4x2 = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0 + -3y2 + 3y2
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-6rt2 + 8rt3xy + 24rt3x2 + -4rt3y2 + r3t + -3r4 + 9xy + -4x2 + 3y2 = 0

The solution to this equation could not be determined.

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