4b^2+17b+15=0

Solution for 4b^2+17b+15=0 equation:

Simplifying
4b2 + 17b + 15 = 0

Reorder the terms:
15 + 17b + 4b2 = 0

Solving
15 + 17b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + b)(5 + 4b) = 0

Subproblem 1
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

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

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

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

Simplifying
b = -3
Subproblem 2
Set the factor '(5 + 4b)' equal to zero and attempt to solve:

Simplifying
5 + 4b = 0

Solving
5 + 4b = 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 + 4b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4b = 0 + -5
4b = 0 + -5

Combine like terms: 0 + -5 = -5
4b = -5

Divide each side by '4'.
b = -1.25

Simplifying
b = -1.25
Solution
b = {-3, -1.25}