b(6b+7)=5

Solution for b(6b+7)=5 equation:

Simplifying
b(6b + 7) = 5

Reorder the terms:
b(7 + 6b) = 5
(7 * b + 6b * b) = 5
(7b + 6b2) = 5

Solving
7b + 6b2 = 5

Solving for variable 'b'.

Reorder the terms:
-5 + 7b + 6b2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 7b + 6b2 = 0

Factor a trinomial.
(-5 + -3b)(1 + -2b) = 0

Subproblem 1
Set the factor '(-5 + -3b)' equal to zero and attempt to solve:

Simplifying
-5 + -3b = 0

Solving
-5 + -3b = 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 + -3b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3b = 0 + 5
-3b = 0 + 5

Combine like terms: 0 + 5 = 5
-3b = 5

Divide each side by '-3'.
b = -1.666666667

Simplifying
b = -1.666666667
Subproblem 2
Set the factor '(1 + -2b)' equal to zero and attempt to solve:

Simplifying
1 + -2b = 0

Solving
1 + -2b = 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 + -2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2b = 0 + -1
-2b = 0 + -1

Combine like terms: 0 + -1 = -1
-2b = -1

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
Solution
b = {-1.666666667, 0.5}