b^2-3b+6=3b+1

Solution for b^2-3b+6=3b+1 equation:

Simplifying
b2 + -3b + 6 = 3b + 1

Reorder the terms:
6 + -3b + b2 = 3b + 1

Reorder the terms:
6 + -3b + b2 = 1 + 3b

Solving
6 + -3b + b2 = 1 + 3b

Solving for variable 'b'.

Reorder the terms:
6 + -1 + -3b + -3b + b2 = 1 + 3b + -1 + -3b

Combine like terms: 6 + -1 = 5
5 + -3b + -3b + b2 = 1 + 3b + -1 + -3b

Combine like terms: -3b + -3b = -6b
5 + -6b + b2 = 1 + 3b + -1 + -3b

Reorder the terms:
5 + -6b + b2 = 1 + -1 + 3b + -3b

Combine like terms: 1 + -1 = 0
5 + -6b + b2 = 0 + 3b + -3b
5 + -6b + b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
5 + -6b + b2 = 0

Factor a trinomial.
(1 + -1b)(5 + -1b) = 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 '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {1, 5}