10b^2+31b+13=-2

Solution for 10b^2+31b+13=-2 equation:

Simplifying
10b2 + 31b + 13 = -2

Reorder the terms:
13 + 31b + 10b2 = -2

Solving
13 + 31b + 10b2 = -2

Solving for variable 'b'.

Reorder the terms:
13 + 2 + 31b + 10b2 = -2 + 2

Combine like terms: 13 + 2 = 15
15 + 31b + 10b2 = -2 + 2

Combine like terms: -2 + 2 = 0
15 + 31b + 10b2 = 0

Factor a trinomial.
(5 + 2b)(3 + 5b) = 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 '(3 + 5b)' equal to zero and attempt to solve:

Simplifying
3 + 5b = 0

Solving
3 + 5b = 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 + 5b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5b = 0 + -3
5b = 0 + -3

Combine like terms: 0 + -3 = -3
5b = -3

Divide each side by '5'.
b = -0.6

Simplifying
b = -0.6
Solution
b = {-2.5, -0.6}