(5v-20)(20v-5)=0

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Solution for (5v-20)(20v-5)=0 equation: 


Simplifying
(5v + -20)(20v + -5) = 0

Reorder the terms:
(-20 + 5v)(20v + -5) = 0

Reorder the terms:
(-20 + 5v)(-5 + 20v) = 0

Multiply (-20 + 5v) * (-5 + 20v)
(-20(-5 + 20v) + 5v * (-5 + 20v)) = 0
((-5 * -20 + 20v * -20) + 5v * (-5 + 20v)) = 0
((100 + -400v) + 5v * (-5 + 20v)) = 0
(100 + -400v + (-5 * 5v + 20v * 5v)) = 0
(100 + -400v + (-25v + 100v2)) = 0

Combine like terms: -400v + -25v = -425v
(100 + -425v + 100v2) = 0

Solving
100 + -425v + 100v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '25'.
25(4 + -17v + 4v2) = 0

Factor a trinomial.
25((1 + -4v)(4 + -1v)) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(1 + -4v)' equal to zero and attempt to solve:

Simplifying
1 + -4v = 0

Solving
1 + -4v = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4v = 0 + -1
-4v = 0 + -1

Combine like terms: 0 + -1 = -1
-4v = -1

Divide each side by '-4'.
v = 0.25

Simplifying
v = 0.25

Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {0.25, 4}

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