2b^2+7b=-3

Solution for 2b^2+7b=-3 equation:

Simplifying
2b2 + 7b = -3

Reorder the terms:
7b + 2b2 = -3

Solving
7b + 2b2 = -3

Solving for variable 'b'.

Reorder the terms:
3 + 7b + 2b2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 7b + 2b2 = 0

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

Subproblem 1
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 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 + b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + b = 0 + -3
b = 0 + -3

Combine like terms: 0 + -3 = -3
b = -3

Simplifying
b = -3
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 = {-3, -0.5}