21b^2+8=-31b

Solution for 21b^2+8=-31b equation:

Simplifying
21b2 + 8 = -31b

Reorder the terms:
8 + 21b2 = -31b

Solving
8 + 21b2 = -31b

Solving for variable 'b'.

Reorder the terms:
8 + 31b + 21b2 = -31b + 31b

Combine like terms: -31b + 31b = 0
8 + 31b + 21b2 = 0

Factor a trinomial.
(8 + 7b)(1 + 3b) = 0

Subproblem 1
Set the factor '(8 + 7b)' equal to zero and attempt to solve:

Simplifying
8 + 7b = 0

Solving
8 + 7b = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7b = 0 + -8
7b = 0 + -8

Combine like terms: 0 + -8 = -8
7b = -8

Divide each side by '7'.
b = -1.142857143

Simplifying
b = -1.142857143
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 = {-1.142857143, -0.3333333333}