6=5b^2+7b

Solution for 6=5b^2+7b equation:

Simplifying
6 = 5b2 + 7b

Reorder the terms:
6 = 7b + 5b2

Solving
6 = 7b + 5b2

Solving for variable 'b'.

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

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

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

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

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

Simplifying
3 + -5b = 0

Solving
3 + -5b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5b = 0 + -3

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

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

Divide each side by '-5'.
b = 0.6

Simplifying
b = 0.6
Subproblem 2
Set the factor '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

Solving
2 + b = 0

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

Add '-2' to each side of the equation.
2 + -2 + b = 0 + -2

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

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

Simplifying
b = -2
Solution
b = {0.6, -2}