=(r-3s+t)(2r-s+t)

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Solution for =(r-3s+t)(2r-s+t) equation: 


Simplifying
0 = (r + -3s + t)(2r + -1s + t)

Multiply (r + -3s + t) * (2r + -1s + t)
0 = (r(2r + -1s + t) + -3s * (2r + -1s + t) + t(2r + -1s + t))
0 = ((2r * r + -1s * r + t * r) + -3s * (2r + -1s + t) + t(2r + -1s + t))

Reorder the terms:
0 = ((-1rs + rt + 2r2) + -3s * (2r + -1s + t) + t(2r + -1s + t))
0 = ((-1rs + rt + 2r2) + -3s * (2r + -1s + t) + t(2r + -1s + t))
0 = (-1rs + rt + 2r2 + (2r * -3s + -1s * -3s + t * -3s) + t(2r + -1s + t))

Reorder the terms:
0 = (-1rs + rt + 2r2 + (-6rs + -3st + 3s2) + t(2r + -1s + t))
0 = (-1rs + rt + 2r2 + (-6rs + -3st + 3s2) + t(2r + -1s + t))
0 = (-1rs + rt + 2r2 + -6rs + -3st + 3s2 + (2r * t + -1s * t + t * t))
0 = (-1rs + rt + 2r2 + -6rs + -3st + 3s2 + (2rt + -1st + t2))

Reorder the terms:
0 = (-1rs + -6rs + rt + 2rt + 2r2 + -3st + -1st + 3s2 + t2)

Combine like terms: -1rs + -6rs = -7rs
0 = (-7rs + rt + 2rt + 2r2 + -3st + -1st + 3s2 + t2)

Combine like terms: rt + 2rt = 3rt
0 = (-7rs + 3rt + 2r2 + -3st + -1st + 3s2 + t2)

Combine like terms: -3st + -1st = -4st
0 = (-7rs + 3rt + 2r2 + -4st + 3s2 + t2)

Solving
0 = -7rs + 3rt + 2r2 + -4st + 3s2 + t2

Solving for variable 'r'.
Remove the zero:
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = -7rs + 3rt + 2r2 + -4st + 3s2 + t2 + 7rs + -3rt + -2r2 + 4st + -3s2 + -1t2

Reorder the terms:
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = -7rs + 7rs + 3rt + -3rt + 2r2 + -2r2 + -4st + 4st + 3s2 + -3s2 + t2 + -1t2

Combine like terms: -7rs + 7rs = 0
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 0 + 3rt + -3rt + 2r2 + -2r2 + -4st + 4st + 3s2 + -3s2 + t2 + -1t2
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 3rt + -3rt + 2r2 + -2r2 + -4st + 4st + 3s2 + -3s2 + t2 + -1t2

Combine like terms: 3rt + -3rt = 0
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 0 + 2r2 + -2r2 + -4st + 4st + 3s2 + -3s2 + t2 + -1t2
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 2r2 + -2r2 + -4st + 4st + 3s2 + -3s2 + t2 + -1t2

Combine like terms: 2r2 + -2r2 = 0
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 0 + -4st + 4st + 3s2 + -3s2 + t2 + -1t2
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = -4st + 4st + 3s2 + -3s2 + t2 + -1t2

Combine like terms: -4st + 4st = 0
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 0 + 3s2 + -3s2 + t2 + -1t2
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 3s2 + -3s2 + t2 + -1t2

Combine like terms: 3s2 + -3s2 = 0
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 0 + t2 + -1t2
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
7rs + -3rt + -2r2 + 4st + -3s2 + -1t2 = 0

The solution to this equation could not be determined.

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