3b^2-18b=b-6

Solution for 3b^2-18b=b-6 equation:

Simplifying
3b2 + -18b = b + -6

Reorder the terms:
-18b + 3b2 = b + -6

Reorder the terms:
-18b + 3b2 = -6 + b

Solving
-18b + 3b2 = -6 + b

Solving for variable 'b'.

Reorder the terms:
6 + -18b + -1b + 3b2 = -6 + b + 6 + -1b

Combine like terms: -18b + -1b = -19b
6 + -19b + 3b2 = -6 + b + 6 + -1b

Reorder the terms:
6 + -19b + 3b2 = -6 + 6 + b + -1b

Combine like terms: -6 + 6 = 0
6 + -19b + 3b2 = 0 + b + -1b
6 + -19b + 3b2 = b + -1b

Combine like terms: b + -1b = 0
6 + -19b + 3b2 = 0

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

Subproblem 1
Set the factor '(1 + -3b)' equal to zero and attempt to solve:

Simplifying
1 + -3b = 0

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

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

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

Divide each side by '-3'.
b = 0.3333333333

Simplifying
b = 0.3333333333
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 = {0.3333333333, 6}