b^2=3b+18

Solution for b^2=3b+18 equation:

Simplifying
b2 = 3b + 18

Reorder the terms:
b2 = 18 + 3b

Solving
b2 = 18 + 3b

Solving for variable 'b'.

Reorder the terms:
-18 + -3b + b2 = 18 + 3b + -18 + -3b

Reorder the terms:
-18 + -3b + b2 = 18 + -18 + 3b + -3b

Combine like terms: 18 + -18 = 0
-18 + -3b + b2 = 0 + 3b + -3b
-18 + -3b + b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-18 + -3b + 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}