(r^2-20tw)(4wr+5tr)=

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Solution for (r^2-20tw)(4wr+5tr)= equation: 


Simplifying
(r2 + -20tw)(4wr + 5tr) = 0

Reorder the terms:
(r2 + -20tw)(5rt + 4rw) = 0

Multiply (r2 + -20tw) * (5rt + 4rw)
(r2(5rt + 4rw) + -20tw * (5rt + 4rw)) = 0
((5rt * r2 + 4rw * r2) + -20tw * (5rt + 4rw)) = 0
((5r3t + 4r3w) + -20tw * (5rt + 4rw)) = 0
(5r3t + 4r3w + (5rt * -20tw + 4rw * -20tw)) = 0

Reorder the terms:
(5r3t + 4r3w + (-80rtw2 + -100rt2w)) = 0
(5r3t + 4r3w + (-80rtw2 + -100rt2w)) = 0

Reorder the terms:
(-80rtw2 + -100rt2w + 5r3t + 4r3w) = 0
(-80rtw2 + -100rt2w + 5r3t + 4r3w) = 0

Solving
-80rtw2 + -100rt2w + 5r3t + 4r3w = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-80tw2 + -100t2w + 5r2t + 4r2w) = 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 '(-80tw2 + -100t2w + 5r2t + 4r2w)' equal to zero and attempt to solve:

Simplifying
-80tw2 + -100t2w + 5r2t + 4r2w = 0

Reorder the terms:
5r2t + 4r2w + -80tw2 + -100t2w = 0

Solving
5r2t + 4r2w + -80tw2 + -100t2w = 0

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

Add '80tw2' to each side of the equation.
5r2t + 4r2w + -80tw2 + 80tw2 + -100t2w = 0 + 80tw2

Combine like terms: -80tw2 + 80tw2 = 0
5r2t + 4r2w + 0 + -100t2w = 0 + 80tw2
5r2t + 4r2w + -100t2w = 0 + 80tw2
Remove the zero:
5r2t + 4r2w + -100t2w = 80tw2

Add '100t2w' to each side of the equation.
5r2t + 4r2w + -100t2w + 100t2w = 80tw2 + 100t2w

Combine like terms: -100t2w + 100t2w = 0
5r2t + 4r2w + 0 = 80tw2 + 100t2w
5r2t + 4r2w = 80tw2 + 100t2w

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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