7b^2+31b+12=0

Solution for 7b^2+31b+12=0 equation:

Simplifying
7b2 + 31b + 12 = 0

Reorder the terms:
12 + 31b + 7b2 = 0

Solving
12 + 31b + 7b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(4 + b)(3 + 7b) = 0

Subproblem 1
Set the factor '(4 + b)' equal to zero and attempt to solve:

Simplifying
4 + b = 0

Solving
4 + b = 0

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

Add '-4' to each side of the equation.
4 + -4 + b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + b = 0 + -4
b = 0 + -4

Combine like terms: 0 + -4 = -4
b = -4

Simplifying
b = -4
Subproblem 2
Set the factor '(3 + 7b)' equal to zero and attempt to solve:

Simplifying
3 + 7b = 0

Solving
3 + 7b = 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 + 7b = 0 + -3

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

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

Divide each side by '7'.
b = -0.4285714286

Simplifying
b = -0.4285714286
Solution
b = {-4, -0.4285714286}