=(r^2-6tw)(3wr-2tr)

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Solution for =(r^2-6tw)(3wr-2tr) equation: 


Simplifying
0 = (r2 + -6tw)(3wr + -2tr)

Reorder the terms:
0 = (r2 + -6tw)(-2rt + 3rw)

Multiply (r2 + -6tw) * (-2rt + 3rw)
0 = (r2(-2rt + 3rw) + -6tw * (-2rt + 3rw))
0 = ((-2rt * r2 + 3rw * r2) + -6tw * (-2rt + 3rw))
0 = ((-2r3t + 3r3w) + -6tw * (-2rt + 3rw))
0 = (-2r3t + 3r3w + (-2rt * -6tw + 3rw * -6tw))

Reorder the terms:
0 = (-2r3t + 3r3w + (-18rtw2 + 12rt2w))
0 = (-2r3t + 3r3w + (-18rtw2 + 12rt2w))

Reorder the terms:
0 = (-18rtw2 + 12rt2w + -2r3t + 3r3w)
0 = (-18rtw2 + 12rt2w + -2r3t + 3r3w)

Solving
0 = -18rtw2 + 12rt2w + -2r3t + 3r3w

Solving for variable 'r'.
Remove the zero:
18rtw2 + -12rt2w + 2r3t + -3r3w = -18rtw2 + 12rt2w + -2r3t + 3r3w + 18rtw2 + -12rt2w + 2r3t + -3r3w

Reorder the terms:
18rtw2 + -12rt2w + 2r3t + -3r3w = -18rtw2 + 18rtw2 + 12rt2w + -12rt2w + -2r3t + 2r3t + 3r3w + -3r3w

Combine like terms: -18rtw2 + 18rtw2 = 0
18rtw2 + -12rt2w + 2r3t + -3r3w = 0 + 12rt2w + -12rt2w + -2r3t + 2r3t + 3r3w + -3r3w
18rtw2 + -12rt2w + 2r3t + -3r3w = 12rt2w + -12rt2w + -2r3t + 2r3t + 3r3w + -3r3w

Combine like terms: 12rt2w + -12rt2w = 0
18rtw2 + -12rt2w + 2r3t + -3r3w = 0 + -2r3t + 2r3t + 3r3w + -3r3w
18rtw2 + -12rt2w + 2r3t + -3r3w = -2r3t + 2r3t + 3r3w + -3r3w

Combine like terms: -2r3t + 2r3t = 0
18rtw2 + -12rt2w + 2r3t + -3r3w = 0 + 3r3w + -3r3w
18rtw2 + -12rt2w + 2r3t + -3r3w = 3r3w + -3r3w

Combine like terms: 3r3w + -3r3w = 0
18rtw2 + -12rt2w + 2r3t + -3r3w = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(18tw2 + -12t2w + 2r2t + -3r2w) = 0


Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0

Subproblem 2
Set the factor '(18tw2 + -12t2w + 2r2t + -3r2w)' equal to zero and attempt to solve:

Simplifying
18tw2 + -12t2w + 2r2t + -3r2w = 0

Reorder the terms:
2r2t + -3r2w + 18tw2 + -12t2w = 0

Solving
2r2t + -3r2w + 18tw2 + -12t2w = 0

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

Add '-18tw2' to each side of the equation.
2r2t + -3r2w + 18tw2 + -18tw2 + -12t2w = 0 + -18tw2

Combine like terms: 18tw2 + -18tw2 = 0
2r2t + -3r2w + 0 + -12t2w = 0 + -18tw2
2r2t + -3r2w + -12t2w = 0 + -18tw2
Remove the zero:
2r2t + -3r2w + -12t2w = -18tw2

Add '12t2w' to each side of the equation.
2r2t + -3r2w + -12t2w + 12t2w = -18tw2 + 12t2w

Combine like terms: -12t2w + 12t2w = 0
2r2t + -3r2w + 0 = -18tw2 + 12t2w
2r2t + -3r2w = -18tw2 + 12t2w

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}

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