Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12.

Quadratic equations are the equations that can have at most two roots. Their degree is equal to two. Let's solve a problem related to it.

Answer: The solutions to the equation (x + 2) (x + 3) = 12 are x = 1 and x = -6.

Let's understand the solution in detail.

Explanation:

We are given the equation (x + 2) (x + 3) = 12.

It can be rewritten as (x + 2) (x + 3) - 12 = 0.

Now, we expand the equation:

⇒ (x + 2) (x + 3) - 12 = 0

⇒ x² + 5x + 6 - 12 = 0

⇒ x² + 5x - 6 = 0

Now, we use splitting the middle term method to represent the above equation in product form:

⇒ x² + 6x - x - 6 = 0

⇒ x(x + 6) - 1(x + 6) = 0

⇒ (x - 1) (x + 6) = 0

Now, we use the zero product property.

We can have two cases:

⇒ x - 1 = 0 or,

⇒ x + 6 = 0

Hence, we have two solutions: x = 1 and x = -6.

Hence, the solutions to the equation (x + 2) (x + 3) = 12 are x = 1 and x = -6.