2b^2=-3b-1

Solution for 2b^2=-3b-1 equation:

Simplifying
2b2 = -3b + -1

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

Solving
2b2 = -1 + -3b

Solving for variable 'b'.

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

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

Combine like terms: -1 + 1 = 0
1 + 3b + 2b2 = 0 + -3b + 3b
1 + 3b + 2b2 = -3b + 3b

Combine like terms: -3b + 3b = 0
1 + 3b + 2b2 = 0

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

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

Simplifying
1 + b = 0

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

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

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

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

Simplifying
1 + 2b = 0

Solving
1 + 2b = 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 + 2b = 0 + -1

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

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

Divide each side by '2'.
b = -0.5

Simplifying
b = -0.5
Solution
b = {-1, -0.5}