3b^2-8b=9-2b

Solution for 3b^2-8b=9-2b equation:

Simplifying
3b2 + -8b = 9 + -2b

Reorder the terms:
-8b + 3b2 = 9 + -2b

Solving
-8b + 3b2 = 9 + -2b

Solving for variable 'b'.

Reorder the terms:
-9 + -8b + 2b + 3b2 = 9 + -2b + -9 + 2b

Combine like terms: -8b + 2b = -6b
-9 + -6b + 3b2 = 9 + -2b + -9 + 2b

Reorder the terms:
-9 + -6b + 3b2 = 9 + -9 + -2b + 2b

Combine like terms: 9 + -9 = 0
-9 + -6b + 3b2 = 0 + -2b + 2b
-9 + -6b + 3b2 = -2b + 2b

Combine like terms: -2b + 2b = 0
-9 + -6b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -2b + b2) = 0

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

Ignore the factor 3.
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}