4b^2-20b-200=0

Solution for 4b^2-20b-200=0 equation:

Simplifying
4b2 + -20b + -200 = 0

Reorder the terms:
-200 + -20b + 4b2 = 0

Solving
-200 + -20b + 4b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + -5b + b2) = 0

Factor a trinomial.
4((-5 + -1b)(10 + -1b)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1b)' equal to zero and attempt to solve:

Simplifying
10 + -1b = 0

Solving
10 + -1b = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1b = 0 + -10
-1b = 0 + -10

Combine like terms: 0 + -10 = -10
-1b = -10

Divide each side by '-1'.
b = 10

Simplifying
b = 10
Solution
b = {-5, 10}