6=2b^2+b

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

Simplifying
6 = 2b2 + b

Reorder the terms:
6 = b + 2b2

Solving
6 = b + 2b2

Solving for variable 'b'.

Reorder the terms:
6 + -1b + -2b2 = b + -1b + 2b2 + -2b2

Combine like terms: b + -1b = 0
6 + -1b + -2b2 = 0 + 2b2 + -2b2
6 + -1b + -2b2 = 2b2 + -2b2

Combine like terms: 2b2 + -2b2 = 0
6 + -1b + -2b2 = 0

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

Subproblem 1
Set the factor '(3 + -2b)' equal to zero and attempt to solve:

Simplifying
3 + -2b = 0

Solving
3 + -2b = 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 + -2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2b = 0 + -3
-2b = 0 + -3

Combine like terms: 0 + -3 = -3
-2b = -3

Divide each side by '-2'.
b = 1.5

Simplifying
b = 1.5
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 = {1.5, -2}