3b^2+10b+12=b^2+b+2

Solution for 3b^2+10b+12=b^2+b+2 equation:

Simplifying
3b2 + 10b + 12 = b2 + b + 2

Reorder the terms:
12 + 10b + 3b2 = b2 + b + 2

Reorder the terms:
12 + 10b + 3b2 = 2 + b + b2

Solving
12 + 10b + 3b2 = 2 + b + b2

Solving for variable 'b'.

Reorder the terms:
12 + -2 + 10b + -1b + 3b2 + -1b2 = 2 + b + b2 + -2 + -1b + -1b2

Combine like terms: 12 + -2 = 10
10 + 10b + -1b + 3b2 + -1b2 = 2 + b + b2 + -2 + -1b + -1b2

Combine like terms: 10b + -1b = 9b
10 + 9b + 3b2 + -1b2 = 2 + b + b2 + -2 + -1b + -1b2

Combine like terms: 3b2 + -1b2 = 2b2
10 + 9b + 2b2 = 2 + b + b2 + -2 + -1b + -1b2

Reorder the terms:
10 + 9b + 2b2 = 2 + -2 + b + -1b + b2 + -1b2

Combine like terms: 2 + -2 = 0
10 + 9b + 2b2 = 0 + b + -1b + b2 + -1b2
10 + 9b + 2b2 = b + -1b + b2 + -1b2

Combine like terms: b + -1b = 0
10 + 9b + 2b2 = 0 + b2 + -1b2
10 + 9b + 2b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
10 + 9b + 2b2 = 0

Factor a trinomial.
(5 + 2b)(2 + b) = 0

Subproblem 1
Set the factor '(5 + 2b)' equal to zero and attempt to solve:

Simplifying
5 + 2b = 0

Solving
5 + 2b = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2b = 0 + -5
2b = 0 + -5

Combine like terms: 0 + -5 = -5
2b = -5

Divide each side by '2'.
b = -2.5

Simplifying
b = -2.5
Subproblem 2
Set the factor '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

Solving
2 + b = 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 + b = 0 + -2

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

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

Simplifying
b = -2
Solution
b = {-2.5, -2}