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

The solution of the equations are -6 and 1

Step-by-step explanation:

* Lets explain how to solve the problem

- We want to find the solution of the equation (x + 2) (x + 3) = 12

- At first lets use the Foil method to multiply the two brackets

 (x + 2) (x + 3) = (x)(x) + (x)(3) + (2)(x) + (2)(3)

 (x + 2) (x + 3) = x² + 3x + 2x + 6 ⇒ add the like term

 (x + 2) (x + 3) = x² + 5x + 6

∵ (x + 2) (x + 3) = 12

∴ x² + 5x + 6 = 12

- Subtract 12 from both sides

∴ x² + 5x - 6 = 0

- Factorize the left hand side

∵ x² = (x)(x)

∵ -6 = 6 × -1

∵ 6x + -1x = 5x

∴ (x + 6)(x - 1) = 0

- Lets use the zero product property

∵ (x + 6)(x - 1) = 0

∴ x + 6 = 0 ⇒ OR ⇒ x - 1 = 0

∵ x + 6 = 0

- Subtract 6 from both sides

∴ x = -6

∵ x - 1 = 0

- Add 1 to both sides

∴ x = 1

∴ The solution of the equations are -6 and 1

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