b^2-6b+9=6-2b

Solution for b^2-6b+9=6-2b equation:

Simplifying
b2 + -6b + 9 = 6 + -2b

Reorder the terms:
9 + -6b + b2 = 6 + -2b

Solving
9 + -6b + b2 = 6 + -2b

Solving for variable 'b'.

Reorder the terms:
9 + -6 + -6b + 2b + b2 = 6 + -2b + -6 + 2b

Combine like terms: 9 + -6 = 3
3 + -6b + 2b + b2 = 6 + -2b + -6 + 2b

Combine like terms: -6b + 2b = -4b
3 + -4b + b2 = 6 + -2b + -6 + 2b

Reorder the terms:
3 + -4b + b2 = 6 + -6 + -2b + 2b

Combine like terms: 6 + -6 = 0
3 + -4b + b2 = 0 + -2b + 2b
3 + -4b + b2 = -2b + 2b

Combine like terms: -2b + 2b = 0
3 + -4b + b2 = 0

Factor a trinomial.
(1 + -1b)(3 + -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 '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {1, 3}