(2r-4s+6t)(2r-4s+6t)=

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Solution for (2r-4s+6t)(2r-4s+6t)= equation: 


Simplifying
(2r + -4s + 6t)(2r + -4s + 6t) = 0

Multiply (2r + -4s + 6t) * (2r + -4s + 6t)
(2r * (2r + -4s + 6t) + -4s * (2r + -4s + 6t) + 6t * (2r + -4s + 6t)) = 0
((2r * 2r + -4s * 2r + 6t * 2r) + -4s * (2r + -4s + 6t) + 6t * (2r + -4s + 6t)) = 0

Reorder the terms:
((-8rs + 12rt + 4r2) + -4s * (2r + -4s + 6t) + 6t * (2r + -4s + 6t)) = 0
((-8rs + 12rt + 4r2) + -4s * (2r + -4s + 6t) + 6t * (2r + -4s + 6t)) = 0
(-8rs + 12rt + 4r2 + (2r * -4s + -4s * -4s + 6t * -4s) + 6t * (2r + -4s + 6t)) = 0

Reorder the terms:
(-8rs + 12rt + 4r2 + (-8rs + -24st + 16s2) + 6t * (2r + -4s + 6t)) = 0
(-8rs + 12rt + 4r2 + (-8rs + -24st + 16s2) + 6t * (2r + -4s + 6t)) = 0
(-8rs + 12rt + 4r2 + -8rs + -24st + 16s2 + (2r * 6t + -4s * 6t + 6t * 6t)) = 0
(-8rs + 12rt + 4r2 + -8rs + -24st + 16s2 + (12rt + -24st + 36t2)) = 0

Reorder the terms:
(-8rs + -8rs + 12rt + 12rt + 4r2 + -24st + -24st + 16s2 + 36t2) = 0

Combine like terms: -8rs + -8rs = -16rs
(-16rs + 12rt + 12rt + 4r2 + -24st + -24st + 16s2 + 36t2) = 0

Combine like terms: 12rt + 12rt = 24rt
(-16rs + 24rt + 4r2 + -24st + -24st + 16s2 + 36t2) = 0

Combine like terms: -24st + -24st = -48st
(-16rs + 24rt + 4r2 + -48st + 16s2 + 36t2) = 0

Solving
-16rs + 24rt + 4r2 + -48st + 16s2 + 36t2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4rs + 6rt + r2 + -12st + 4s2 + 9t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-4rs + 6rt + r2 + -12st + 4s2 + 9t2)' equal to zero and attempt to solve:

Simplifying
-4rs + 6rt + r2 + -12st + 4s2 + 9t2 = 0

Solving
-4rs + 6rt + r2 + -12st + 4s2 + 9t2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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