b(10b+1)=9

Solution for b(10b+1)=9 equation:

Simplifying
b(10b + 1) = 9

Reorder the terms:
b(1 + 10b) = 9
(1 * b + 10b * b) = 9
(1b + 10b2) = 9

Solving
1b + 10b2 = 9

Solving for variable 'b'.

Reorder the terms:
-9 + 1b + 10b2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 1b + 10b2 = 0

Factor a trinomial.
(-1 + -1b)(9 + -10b) = 0

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 '(9 + -10b)' equal to zero and attempt to solve:

Simplifying
9 + -10b = 0

Solving
9 + -10b = 0

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

Add '-9' to each side of the equation.
9 + -9 + -10b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -10b = 0 + -9
-10b = 0 + -9

Combine like terms: 0 + -9 = -9
-10b = -9

Divide each side by '-10'.
b = 0.9

Simplifying
b = 0.9
Solution
b = {-1, 0.9}