(4b-20)(20b-4)=0

Solution for (4b-20)(20b-4)=0 equation:

Simplifying
(4b + -20)(20b + -4) = 0

Reorder the terms:
(-20 + 4b)(20b + -4) = 0

Reorder the terms:
(-20 + 4b)(-4 + 20b) = 0

Multiply (-20 + 4b) * (-4 + 20b)
(-20(-4 + 20b) + 4b * (-4 + 20b)) = 0
((-4 * -20 + 20b * -20) + 4b * (-4 + 20b)) = 0
((80 + -400b) + 4b * (-4 + 20b)) = 0
(80 + -400b + (-4 * 4b + 20b * 4b)) = 0
(80 + -400b + (-16b + 80b2)) = 0

Combine like terms: -400b + -16b = -416b
(80 + -416b + 80b2) = 0

Solving
80 + -416b + 80b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '16'.
16(5 + -26b + 5b2) = 0

Factor a trinomial.
16((1 + -5b)(5 + -1b)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(1 + -5b)' equal to zero and attempt to solve:

Simplifying
1 + -5b = 0

Solving
1 + -5b = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5b = 0 + -1
-5b = 0 + -1

Combine like terms: 0 + -1 = -1
-5b = -1

Divide each side by '-5'.
b = 0.2

Simplifying
b = 0.2
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {0.2, 5}