4b(3b+6)=-9

Solution for 4b(3b+6)=-9 equation:

Simplifying
4b(3b + 6) = -9

Reorder the terms:
4b(6 + 3b) = -9
(6 * 4b + 3b * 4b) = -9
(24b + 12b2) = -9

Solving
24b + 12b2 = -9

Solving for variable 'b'.

Reorder the terms:
9 + 24b + 12b2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + 24b + 12b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 8b + 4b2) = 0

Factor a trinomial.
3((3 + 2b)(1 + 2b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 2b)' equal to zero and attempt to solve:

Simplifying
3 + 2b = 0

Solving
3 + 2b = 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 + 2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2b = 0 + -3
2b = 0 + -3

Combine like terms: 0 + -3 = -3
2b = -3

Divide each side by '2'.
b = -1.5

Simplifying
b = -1.5
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 = {-1.5, -0.5}