b^2=9b-18

Solution for b^2=9b-18 equation:

Simplifying
b2 = 9b + -18

Reorder the terms:
b2 = -18 + 9b

Solving
b2 = -18 + 9b

Solving for variable 'b'.

Reorder the terms:
18 + -9b + b2 = -18 + 9b + 18 + -9b

Reorder the terms:
18 + -9b + b2 = -18 + 18 + 9b + -9b

Combine like terms: -18 + 18 = 0
18 + -9b + b2 = 0 + 9b + -9b
18 + -9b + b2 = 9b + -9b

Combine like terms: 9b + -9b = 0
18 + -9b + b2 = 0

Factor a trinomial.
(3 + -1b)(6 + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

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

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

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {3, 6}