What values of b satisfy 3(2b + 3)² = 36?
b = (2√3 - 3)/2, b = (-3√3 - 2)/2, b = (-2√3 - 3)/2, b = (-2√3 + 3)/2 

Solution:

An equation is a mathematical statement with an ‘equal to’ symbol between two algebraic expressions that have equal values.

An equation consists of algebraic expressions on both sides of the equal sign. If we add or subtract the same number from both sides of an equation, it still holds.

3 (2b + 3)² = 36

⇒ (2b + 3)² = 36/3

⇒ (2b + 3)² = 12

⇒ 2b + 3 = ± 2√3

⇒ 2b = ± 2√3 – 3

⇒ b = (± 2√3 – 3)/2

⇒ b = (2√3 – 3)/2, b = (-2√3 – 3)/2

So, the required values of b are (2√3 – 3)/2 and (-2√3 + 3)/2.

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

Summary:

The values of b = (2√3 - 3)/2, b = (- 2√3 - 3)/2 which satisfy 3(2b + 3)² = 36