Solve using the zero product property. Be sure each equation is in standard form and factor out any common factors before attempting to solve. Check all answers in the original equation. (m + 5)(m + 6) = 6
A) m = -5, m = -6
B) m = 1, m = 0
C) m = -8, m = -3
D) m = 8, m = 3

Question

Quizplus · Accepted Answer

First, distribute the left side of the equation:
m^2 + 11m + 30 = 6
Next, move all terms to one side:
m^2 + 11m + 24 = 0
Now factor:
(m + 8)(m + 3) = 0
By the zero product property, we know that:
m + 8 = 0 or m + 3 = 0
Solving each equation gives us the solutions:
m = -8 or m = -3
We need to check these solutions in the original equation:
(m + 5)(m + 6) = 6
(-8 + 5)(-8 + 6) = 6 is false
(-3 + 5)(-3 + 6) = 6 is true
Therefore, the final solution is:
m = -3.

Solve Using the Zero Product Property