4b^2+12b+9=0

Solution for 4b^2+12b+9=0 equation:

Simplifying
4b2 + 12b + 9 = 0

Reorder the terms:
9 + 12b + 4b2 = 0

Solving
9 + 12b + 4b2 = 0

Solving for variable 'b'.

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

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 '(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
Solution
b = {-1.5, -1.5}