b(8b+1)=7

Solution for b(8b+1)=7 equation:

Simplifying
b(8b + 1) = 7

Reorder the terms:
b(1 + 8b) = 7
(1 * b + 8b * b) = 7
(1b + 8b2) = 7

Solving
1b + 8b2 = 7

Solving for variable 'b'.

Reorder the terms:
-7 + 1b + 8b2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 1b + 8b2 = 0

Factor a trinomial.
(-1 + -1b)(7 + -8b) = 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 '(7 + -8b)' equal to zero and attempt to solve:

Simplifying
7 + -8b = 0

Solving
7 + -8b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8b = 0 + -7
-8b = 0 + -7

Combine like terms: 0 + -7 = -7
-8b = -7

Divide each side by '-8'.
b = 0.875

Simplifying
b = 0.875
Solution
b = {-1, 0.875}