9b^2+24b+7=0

Solution for 9b^2+24b+7=0 equation:

Simplifying
9b2 + 24b + 7 = 0

Reorder the terms:
7 + 24b + 9b2 = 0

Solving
7 + 24b + 9b2 = 0

Solving for variable 'b'.

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

Subproblem 1
Set the factor '(7 + 3b)' equal to zero and attempt to solve:

Simplifying
7 + 3b = 0

Solving
7 + 3b = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3b = 0 + -7

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

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

Divide each side by '3'.
b = -2.333333333

Simplifying
b = -2.333333333
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 = {-2.333333333, -0.3333333333}