2b^2-12b+6=-3b-b^2

Solution for 2b^2-12b+6=-3b-b^2 equation:

Simplifying
2b2 + -12b + 6 = -3b + -1b2

Reorder the terms:
6 + -12b + 2b2 = -3b + -1b2

Solving
6 + -12b + 2b2 = -3b + -1b2

Solving for variable 'b'.

Reorder the terms:
6 + -12b + 3b + 2b2 + b2 = -3b + -1b2 + 3b + b2

Combine like terms: -12b + 3b = -9b
6 + -9b + 2b2 + b2 = -3b + -1b2 + 3b + b2

Combine like terms: 2b2 + b2 = 3b2
6 + -9b + 3b2 = -3b + -1b2 + 3b + b2

Reorder the terms:
6 + -9b + 3b2 = -3b + 3b + -1b2 + b2

Combine like terms: -3b + 3b = 0
6 + -9b + 3b2 = 0 + -1b2 + b2
6 + -9b + 3b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
6 + -9b + 3b2 = 0

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

Factor a trinomial.
3((1 + -1b)(2 + -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 '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {1, 2}