What values of b satisfy 3(2b + 3)^2 = 36?

Answer:
either b = -1.5 + √3
or b = -1.5 - √3

Explanation:
To solve this problem, we will simplify the expression on the left-hand side and solve for "b" as follows:
The given expression is:
3(2b+3)² = 36

1- Divide both sides of the equation by 3. This will give:
(2b+3)² = 12

2- Expand the bracket as follows:
(2b+3)² = 12
(2b)² + 2(2b)(3) + (3)² = 12
4b² + 12b + 9 = 12

3- Put the equation is standard form (ax² + bx + c = 0):
4b² + 12b + 9 = 12
4b² + 12b + 9 - 12 = 0
4b² + 12b - 3 = 0

4- Factorize the equation to get the values of "b":
4b² + 12b - 3 = 0
By comparing the given equation with the standard form, we will find that:
a = 4
b = 12 
c = -3
Use the quadratic formula shown in the attached image, substitute with the values of a, b and c and solve for "b"
This will give us:
either b = -1.5 + √3
or b = -1.5 - √3

Hope this helps :)