3b^2+31b+10=0

Solution for 3b^2+31b+10=0 equation:

Simplifying
3b2 + 31b + 10 = 0

Reorder the terms:
10 + 31b + 3b2 = 0

Solving
10 + 31b + 3b2 = 0

Solving for variable 'b'.

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

Subproblem 1
Set the factor '(10 + b)' equal to zero and attempt to solve:

Simplifying
10 + b = 0

Solving
10 + b = 0

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

Add '-10' to each side of the equation.
10 + -10 + b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + b = 0 + -10
b = 0 + -10

Combine like terms: 0 + -10 = -10
b = -10

Simplifying
b = -10
Subproblem 2
Set the factor '(1 + 3b)' equal to zero and attempt to solve:

Simplifying
1 + 3b = 0

Solving
1 + 3b = 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 + 3b = 0 + -1

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

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

Divide each side by '3'.
b = -0.3333333333

Simplifying
b = -0.3333333333
Solution
b = {-10, -0.3333333333}