Question

what are the solutions to (m+2)(m+3) = 12? Select all that apply.

m = -4

m = 6

m = 1

m = 10

m = 4

m = 9

m = -6

m = -1

Answer 1

how did you get the answer

Answer 2

m = 1

m = -6

Answer 3

To solve the equation (m+2)(m+3) = 12, we first expand and simplify the left side:

(m+2)(m+3) = 12
m^2 + 3m + 2m + 6 = 12
m^2 + 5m + 6 = 12
m^2 + 5m + 6 - 12 = 0
m^2 + 5m - 6 = 0

Now, we can factor the quadratic equation or use the quadratic formula to find the solutions. In this case, the factors of -6 that add up to +5 are +6 and -1. Therefore, the equation becomes:

(m + 6)(m - 1) = 0

Setting each factor to zero gives us the potential solutions:
m + 6 = 0 or m - 1 = 0
m = -6 or m = 1

Therefore, the solutions are:
m = -6
m = 1