3b+2=b^2-8

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

Simplifying
3b + 2 = b2 + -8

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

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

Solving
2 + 3b = -8 + b2

Solving for variable 'b'.

Reorder the terms:
2 + 8 + 3b + -1b2 = -8 + b2 + 8 + -1b2

Combine like terms: 2 + 8 = 10
10 + 3b + -1b2 = -8 + b2 + 8 + -1b2

Reorder the terms:
10 + 3b + -1b2 = -8 + 8 + b2 + -1b2

Combine like terms: -8 + 8 = 0
10 + 3b + -1b2 = 0 + b2 + -1b2
10 + 3b + -1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
10 + 3b + -1b2 = 0

Factor a trinomial.
(5 + -1b)(2 + b) = 0

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

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 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 = {5, -2}