(45+50b)b=5

Solution for (45+50b)b=5 equation:

Simplifying
(45 + 50b) * b = 5

Reorder the terms for easier multiplication:
b(45 + 50b) = 5
(45 * b + 50b * b) = 5
(45b + 50b2) = 5

Solving
45b + 50b2 = 5

Solving for variable 'b'.

Reorder the terms:
-5 + 45b + 50b2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 45b + 50b2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 9b + 10b2) = 0

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

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 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 + -1b = 0 + 1

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

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

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

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

Simplifying
1 + -10b = 0

Solving
1 + -10b = 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 + -10b = 0 + -1

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

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

Divide each side by '-10'.
b = 0.1

Simplifying
b = 0.1
Solution
b = {-1, 0.1}