12s^2t^2-8s^2t-9rt^2+6rt=0

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Solution for 12s^2t^2-8s^2t-9rt^2+6rt=0 equation: 


Simplifying
12s2t2 + -8s2t + -9rt2 + 6rt = 0

Reorder the terms:
6rt + -9rt2 + -8s2t + 12s2t2 = 0

Solving
6rt + -9rt2 + -8s2t + 12s2t2 = 0

Solving for variable 'r'.

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

Add '8s2t' to each side of the equation.
6rt + -9rt2 + -8s2t + 8s2t + 12s2t2 = 0 + 8s2t

Combine like terms: -8s2t + 8s2t = 0
6rt + -9rt2 + 0 + 12s2t2 = 0 + 8s2t
6rt + -9rt2 + 12s2t2 = 0 + 8s2t
Remove the zero:
6rt + -9rt2 + 12s2t2 = 8s2t

Add '-12s2t2' to each side of the equation.
6rt + -9rt2 + 12s2t2 + -12s2t2 = 8s2t + -12s2t2

Combine like terms: 12s2t2 + -12s2t2 = 0
6rt + -9rt2 + 0 = 8s2t + -12s2t2
6rt + -9rt2 = 8s2t + -12s2t2

Reorder the terms:
6rt + -9rt2 + -8s2t + 12s2t2 = 8s2t + -8s2t + -12s2t2 + 12s2t2

Combine like terms: 8s2t + -8s2t = 0
6rt + -9rt2 + -8s2t + 12s2t2 = 0 + -12s2t2 + 12s2t2
6rt + -9rt2 + -8s2t + 12s2t2 = -12s2t2 + 12s2t2

Combine like terms: -12s2t2 + 12s2t2 = 0
6rt + -9rt2 + -8s2t + 12s2t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(6r + -9rt + -8s2 + 12s2t) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Add '-1t' to each side of the equation.
t + -1t = 0 + -1t
Remove the zero:
0 = -1t

Simplifying
0 = -1t

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(6r + -9rt + -8s2 + 12s2t)' equal to zero and attempt to solve:

Simplifying
6r + -9rt + -8s2 + 12s2t = 0

Solving
6r + -9rt + -8s2 + 12s2t = 0

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

Add '8s2' to each side of the equation.
6r + -9rt + -8s2 + 8s2 + 12s2t = 0 + 8s2

Combine like terms: -8s2 + 8s2 = 0
6r + -9rt + 0 + 12s2t = 0 + 8s2
6r + -9rt + 12s2t = 0 + 8s2
Remove the zero:
6r + -9rt + 12s2t = 8s2

Add '-12s2t' to each side of the equation.
6r + -9rt + 12s2t + -12s2t = 8s2 + -12s2t

Combine like terms: 12s2t + -12s2t = 0
6r + -9rt + 0 = 8s2 + -12s2t
6r + -9rt = 8s2 + -12s2t

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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