r(z^5-20)(z^5-20)=

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Solution for r(z^5-20)(z^5-20)= equation: 


Simplifying
r(z5 + -20)(z5 + -20) = 0

Reorder the terms:
r(-20 + z5)(z5 + -20) = 0

Reorder the terms:
r(-20 + z5)(-20 + z5) = 0

Multiply (-20 + z5) * (-20 + z5)
r(-20(-20 + z5) + z5(-20 + z5)) = 0
r((-20 * -20 + z5 * -20) + z5(-20 + z5)) = 0
r((400 + -20z5) + z5(-20 + z5)) = 0
r(400 + -20z5 + (-20 * z5 + z5 * z5)) = 0
r(400 + -20z5 + (-20z5 + z10)) = 0

Combine like terms: -20z5 + -20z5 = -40z5
r(400 + -40z5 + z10) = 0
(400 * r + -40z5 * r + z10 * r) = 0
(400r + -40rz5 + rz10) = 0

Solving
400r + -40rz5 + rz10 = 0

Solving for variable 'r'.

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

Factor out the Greatest Common Factor (GCF), 'r'.
r(400 + -40z5 + z10) = 0

Factor a trinomial.
r((20 + -1z5)(20 + -1z5)) = 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 '(20 + -1z5)' equal to zero and attempt to solve:

Simplifying
20 + -1z5 = 0

Solving
20 + -1z5 = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1z5 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1z5 = 0 + -20
-1z5 = 0 + -20

Combine like terms: 0 + -20 = -20
-1z5 = -20

Add 'z5' to each side of the equation.
-1z5 + z5 = -20 + z5

Combine like terms: -1z5 + z5 = 0
0 = -20 + z5

Simplifying
0 = -20 + z5

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(20 + -1z5)' equal to zero and attempt to solve:

Simplifying
20 + -1z5 = 0

Solving
20 + -1z5 = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1z5 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1z5 = 0 + -20
-1z5 = 0 + -20

Combine like terms: 0 + -20 = -20
-1z5 = -20

Add 'z5' to each side of the equation.
-1z5 + z5 = -20 + z5

Combine like terms: -1z5 + z5 = 0
0 = -20 + z5

Simplifying
0 = -20 + z5

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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