4b^2+24b+11=0

Solution for 4b^2+24b+11=0 equation:

Simplifying
4b2 + 24b + 11 = 0

Reorder the terms:
11 + 24b + 4b2 = 0

Solving
11 + 24b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(11 + 2b)(1 + 2b) = 0

Subproblem 1
Set the factor '(11 + 2b)' equal to zero and attempt to solve:

Simplifying
11 + 2b = 0

Solving
11 + 2b = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2b = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2b = 0 + -11
2b = 0 + -11

Combine like terms: 0 + -11 = -11
2b = -11

Divide each side by '2'.
b = -5.5

Simplifying
b = -5.5
Subproblem 2
Set the factor '(1 + 2b)' equal to zero and attempt to solve:

Simplifying
1 + 2b = 0

Solving
1 + 2b = 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 + 2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2b = 0 + -1
2b = 0 + -1

Combine like terms: 0 + -1 = -1
2b = -1

Divide each side by '2'.
b = -0.5

Simplifying
b = -0.5
Solution
b = {-5.5, -0.5}