3b^2+17b=-20

Solution for 3b^2+17b=-20 equation:

Simplifying
3b2 + 17b = -20

Reorder the terms:
17b + 3b2 = -20

Solving
17b + 3b2 = -20

Solving for variable 'b'.

Reorder the terms:
20 + 17b + 3b2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + 17b + 3b2 = 0

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

Simplifying
5 + 3b = 0

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

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

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

Divide each side by '3'.
b = -1.666666667

Simplifying
b = -1.666666667
Solution
b = {-4, -1.666666667}