b^2-3b=3b+27

Solution for b^2-3b=3b+27 equation:

Simplifying
b2 + -3b = 3b + 27

Reorder the terms:
-3b + b2 = 3b + 27

Reorder the terms:
-3b + b2 = 27 + 3b

Solving
-3b + b2 = 27 + 3b

Solving for variable 'b'.

Reorder the terms:
-27 + -3b + -3b + b2 = 27 + 3b + -27 + -3b

Combine like terms: -3b + -3b = -6b
-27 + -6b + b2 = 27 + 3b + -27 + -3b

Reorder the terms:
-27 + -6b + b2 = 27 + -27 + 3b + -3b

Combine like terms: 27 + -27 = 0
-27 + -6b + b2 = 0 + 3b + -3b
-27 + -6b + b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-27 + -6b + b2 = 0

Factor a trinomial.
(-3 + -1b)(9 + -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 '(9 + -1b)' equal to zero and attempt to solve:

Simplifying
9 + -1b = 0

Solving
9 + -1b = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1b = 0 + -9
-1b = 0 + -9

Combine like terms: 0 + -9 = -9
-1b = -9

Divide each side by '-1'.
b = 9

Simplifying
b = 9
Solution
b = {-3, 9}