b(30b+1)=20

Solution for b(30b+1)=20 equation:

Simplifying
b(30b + 1) = 20

Reorder the terms:
b(1 + 30b) = 20
(1 * b + 30b * b) = 20
(1b + 30b2) = 20

Solving
1b + 30b2 = 20

Solving for variable 'b'.

Reorder the terms:
-20 + 1b + 30b2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 1b + 30b2 = 0

Factor a trinomial.
(-5 + -6b)(4 + -5b) = 0

Subproblem 1
Set the factor '(-5 + -6b)' equal to zero and attempt to solve:

Simplifying
-5 + -6b = 0

Solving
-5 + -6b = 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 + -6b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6b = 0 + 5
-6b = 0 + 5

Combine like terms: 0 + 5 = 5
-6b = 5

Divide each side by '-6'.
b = -0.8333333333

Simplifying
b = -0.8333333333
Subproblem 2
Set the factor '(4 + -5b)' equal to zero and attempt to solve:

Simplifying
4 + -5b = 0

Solving
4 + -5b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5b = 0 + -4
-5b = 0 + -4

Combine like terms: 0 + -4 = -4
-5b = -4

Divide each side by '-5'.
b = 0.8

Simplifying
b = 0.8
Solution
b = {-0.8333333333, 0.8}