Answer:
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
