5b^2-75b+250=0

Solution for 5b^2-75b+250=0 equation:

Simplifying
5b2 + -75b + 250 = 0

Reorder the terms:
250 + -75b + 5b2 = 0

Solving
250 + -75b + 5b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(50 + -15b + b2) = 0

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

Ignore the factor 5.
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}